SAT Math Flashcards: Properties Of Right Triangles

What this deck covers

This deck focuses on Properties Of Right Triangles, giving you a quick way to review the definitions, rules, and examples that matter most for SAT Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Find the longer leg in a 30-60-90 triangle with shorter leg $3$.

Answer: $3 \sqrt{3}$. Longer leg equals shorter leg times $\sqrt{3}$.

Flashcard 2: Find the missing leg if $a = 9$, $c = 15$ in a right triangle.

Answer: $b = 12$. Using $9^2 + b^2 = 15^2$, so $b^2 = 144$.

Flashcard 3: If $\text{sin } A = 0.6$, find $\text{cos } A$ in a right triangle.

Answer: $\text{cos } A = 0.8$. Using $\sin^2 A + \cos^2 A = 1$ identity.

Flashcard 4: What is the formula for the area of a right triangle?

Answer: $\frac{1}{2} \times \text{base} \times \text{height}$. Uses the two perpendicular sides as base and height.

Flashcard 5: Find the other side if one leg is $5$ in a 45-45-90 triangle.

Answer: $5$. Both legs are equal in isosceles right triangle.

Flashcard 6: What is the value of $\text{sin } 30^\text{o}$?

Answer: $\frac{1}{2}$. Standard trigonometric value for 30-degree angle.

Flashcard 7: Find the hypotenuse if each leg is $7$ in a 45-45-90 triangle.

Answer: $7\text{√}2$. Hypotenuse equals leg times $\sqrt{2}$ in 45-45-90 triangle.

Flashcard 8: State the sine function definition in a right triangle.

Answer: $\text{sin}(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. Sine relates the side opposite to the angle with the hypotenuse.

Flashcard 9: State the tangent function definition in a right triangle.

Answer: $\text{tan}(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Tangent is the ratio of opposite side to adjacent side.

Flashcard 10: If $\text{tan } A = 1$, what is angle $A$?

Answer: $45^\text{o}$. Angle whose tangent equals 1 is 45 degrees.

Flashcard 11: Find $\text{tan } A$ if $\text{sin } A = 0.8$ and $\text{cos } A = 0.6$.

Answer: $\text{tan } A = \frac{4}{3}$. Tangent equals sine divided by cosine.

Flashcard 12: State the formula for the hypotenuse in a right triangle with legs $a$ and $b$.

Answer: $c = \sqrt{a^2 + b^2}$. Square root of sum of squared legs gives hypotenuse.

Flashcard 13: Identify the complementary angle to 60 degrees in a right triangle.

Answer: 30 degrees. Complementary angles in a right triangle sum to 90 degrees.

Flashcard 14: Which trigonometric function is equal to $\frac{1}{\text{tan } A}$?

Answer: Cotangent. Reciprocal trigonometric function of tangent.

Flashcard 15: Identify the angle opposite the longest side in a right triangle.

Answer: 90 degrees. Right angle is always opposite the hypotenuse.

Flashcard 16: If $\text{sin } A = 0.6$, find $\text{cos } A$ in a right triangle.

Answer: $\text{cos } A = 0.8$. Using $\sin^2 A + \cos^2 A = 1$ identity.

Flashcard 17: What is the cosine of angle $A$ in a right triangle?

Answer: $\frac{\text{adjacent}}{\text{hypotenuse}}$. Ratio of side adjacent to angle to hypotenuse.

Flashcard 18: What is the area formula for a right triangle with base $b$ and height $h$?

Answer: $\frac{1}{2} \times b \times h$. Standard area formula for triangles using base and height.

Flashcard 19: State the sine function definition in a right triangle.

Answer: $\text{sin}(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. Sine relates the side opposite to the angle with the hypotenuse.

Flashcard 20: Find the length of the shorter leg in a 30-60-90 triangle with hypotenuse $10$.

Answer: $5$. Shorter leg is half the hypotenuse in 30-60-90 triangle.

Flashcard 21: Find side $a$ if $b = 6$, $c = 10$ in a right triangle.

Answer: $a = 8$. Using $a^2 + 6^2 = 10^2$, so $a^2 = 64$.

Flashcard 22: What is the tangent of angle $A$ in a right triangle?

Answer: $\frac{\text{opposite}}{\text{adjacent}}$. Ratio of opposite side to adjacent side.

Flashcard 23: Find the length of the hypotenuse in a right triangle with legs $5$ and $12$.

Answer: $c = 13$. Using $5^2 + 12^2 = 25 + 144 = 169$.

Flashcard 24: Calculate the tangent of angle $\theta$ given opposite = 5, adjacent = 12.

Answer: $\tan(\theta) = \frac{5}{12}$. Tangent equals opposite divided by adjacent: $\frac{5}{12}$.

Flashcard 25: What is the sine of angle $A$ in a right triangle?

Answer: $\frac{\text{opposite}}{\text{hypotenuse}}$. Ratio of side opposite angle to longest side.

Flashcard 26: What theorem states that $a^2 + b^2 = c^2$ in a right triangle?

Answer: Pythagorean Theorem. Fundamental relationship between sides in right triangles.

Flashcard 27: What is the reciprocal of $\text{cos } A$?

Answer: Secant. Secant is the reciprocal of cosine function.

Flashcard 28: Which trigonometric function equals $\frac{1}{2}$ at 30 degrees?

Answer: Sine. In a 30-60-90 triangle, $\sin(30°) = \frac{1}{2}$.

Flashcard 29: Which trigonometric function is equal to $\frac{1}{\cos A}$?

Answer: Secant. Reciprocal trigonometric function of cosine.

Flashcard 30: Identify the hypotenuse in a right triangle with sides 3, 4, and 5.

Answer:

1. The hypotenuse is always the longest side, opposite the right angle.

Flashcard 31: State the formula for the hypotenuse in a right triangle with legs $a$ and $b$.

Answer: $c = \sqrt{a^2 + b^2}$. Square root of sum of squared legs gives hypotenuse.

Flashcard 32: What is the formula for the area of a right triangle?

Answer: $\frac{1}{2} \times \text{base} \times \text{height}$. Uses the two perpendicular sides as base and height.

Flashcard 33: Find the length of the shorter leg in a 30-60-90 triangle with hypotenuse $10$.

Answer: $5$. Shorter leg is half the hypotenuse in 30-60-90 triangle.

Flashcard 34: Which trigonometric function is equal to $\frac{1}{\sin A}$?

Answer: Cosecant. Reciprocal trigonometric function of sine.

Flashcard 35: What is the ratio of sides in a 45-45-90 triangle?

Answer: $1:1:\text{√}2$. Special ratio for isosceles right triangle.

Flashcard 36: What is the reciprocal of $\text{tan } A$?

Answer: Cotangent. Cotangent is the reciprocal of tangent function.

Flashcard 37: What is the value of $\text{cot } 45^\text{o}$?

Answer:

1. Cotangent of 45 degrees equals cos 45 divided by sin 45.

Flashcard 38: What is the value of $\text{sec } 0^\text{o}$?

Answer:

1. Secant of 0 degrees equals 1 divided by cos 0.

Flashcard 39: Calculate the tangent of angle $\theta$ given opposite = 5, adjacent = 12.

Answer: $\tan(\theta) = \frac{5}{12}$. Tangent equals opposite divided by adjacent: $\frac{5}{12}$.

Flashcard 40: What is the ratio of sides in a 45-45-90 triangle?

Answer: $1:1:\text{√}2$. Special ratio for isosceles right triangle.

Flashcard 41: What is the value of $\text{sin } 90^\text{o}$?

Answer:

1. Sine of 90 degrees equals 1.

Flashcard 42: What is the value of $\text{sin } 30^\text{o}$?

Answer: $\frac{1}{2}$. Standard trigonometric value for 30-degree angle.

Flashcard 43: State the relationship between the angles in a right triangle.

Answer: Sum is $180^\text{o}$. All triangle angles sum to 180 degrees.

Flashcard 44: Calculate the hypotenuse: $a = 9$, $b = 12$.

Answer: $c = 15$. Using $9^2 + 12^2 = 81 + 144 = 225$.

Flashcard 45: What is the cosine function definition in a right triangle?

Answer: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$. Cosine relates the side adjacent to the angle with the hypotenuse.

Flashcard 46: What is the value of $\text{sec } 0^\text{o}$?

Answer:

1. Secant of 0 degrees equals 1 divided by cos 0.

Flashcard 47: Identify the angle opposite the longest side in a right triangle.

Answer: 90 degrees. Right angle is always opposite the hypotenuse.

Flashcard 48: State the relationship between the angles in a right triangle.

Answer: Sum is $180^\text{o}$. All triangle angles sum to 180 degrees.

Flashcard 49: Find the length of the hypotenuse in a right triangle with legs $5$ and $12$.

Answer: $c = 13$. Using $5^2 + 12^2 = 25 + 144 = 169$.

Flashcard 50: What is the value of $\text{cot } 45^\text{o}$?

Answer:

1. Cotangent of 45 degrees equals cos 45 divided by sin 45.

Flashcard 51: What is the value of $\text{cos } 60^\text{o}$?

Answer: $\frac{1}{2}$. Standard trigonometric value for 60-degree angle.

Flashcard 52: What is the side ratio for a 30-60-90 triangle?

Answer: $1:\text{√}3:2$. Standard side ratio for 30-60-90 special right triangle.

Flashcard 53: What is the reciprocal of $\text{tan } A$?

Answer: Cotangent. Cotangent is the reciprocal of tangent function.

Flashcard 54: If $\text{tan } A = 1$, what is angle $A$?

Answer: $45^\text{o}$. Angle whose tangent equals 1 is 45 degrees.

Flashcard 55: Find the missing side: $b = 8$, $c = 10$ in a right triangle.

Answer: $a = 6$. Using $a^2 + 8^2 = 10^2$, so $a^2 = 36$.

Flashcard 56: Find $\text{tan } A$ if $\text{sin } A = 0.8$ and $\text{cos } A = 0.6$.

Answer: $\text{tan } A = \frac{4}{3}$. Tangent equals sine divided by cosine.

Flashcard 57: What is the side ratio for a 30-60-90 triangle?

Answer: $1 : \sqrt{3} : 2$. Standard side ratio for 30-60-90 special right triangle.

Flashcard 58: Identify the complementary angle to 60 degrees in a right triangle.

Answer: 30 degrees. Complementary angles in a right triangle sum to 90 degrees.

Flashcard 59: Find the missing leg if $a = 9$, $c = 15$ in a right triangle.

Answer: $b = 12$. Using $9^2 + b^2 = 15^2$, so $b^2 = 144$.

Flashcard 60: What is the value of $\text{csc } 90^\text{o}$?

Answer:

1. Cosecant of 90 degrees equals 1 divided by sin 90.

Flashcard 61: What is the relation of angles in a 45-45-90 triangle?

Answer: Each angle is $45^\text{o}$. Isosceles right triangle has two equal acute angles.

Flashcard 62: What is the relation of angles in a 45-45-90 triangle?

Answer: Each angle is $45^\text{o}$. Isosceles right triangle has two equal acute angles.

Flashcard 63: What is the value of $\text{tan } 45^\text{o}$?

Answer:

1. Tangent equals 1 when opposite equals adjacent.

Flashcard 64: What is the value of $\text{csc } 90^\text{o}$?

Answer:

1. Cosecant of 90 degrees equals 1 divided by sin 90.

Flashcard 65: Calculate the tangent of a 45-degree angle in a right triangle.

Answer:

1. In a 45-45-90 triangle, opposite and adjacent sides are equal.

Flashcard 66: What is the reciprocal of $\text{cos } A$?

Answer: Secant. Secant is the reciprocal of cosine function.

Flashcard 67: What is the value of $\text{sin } 90^\text{o}$?

Answer:

1. Sine of 90 degrees equals 1.

Flashcard 68: State the tangent function definition in a right triangle.

Answer: $\text{tan}(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Tangent is the ratio of opposite side to adjacent side.

Flashcard 69: Find the length of the hypotenuse: $a = 3$, $b = 4$.

Answer: $c = 5$. Using $3^2 + 4^2 = 9 + 16 = 25$, so $c = 5$.

Flashcard 70: What is the reciprocal of $\text{sin } A$?

Answer: Cosecant. Cosecant is the reciprocal of sine function.

Flashcard 71: Which trigonometric function is equal to $\frac{1}{\text{tan } A}$?

Answer: Cotangent. Reciprocal trigonometric function of tangent.

Flashcard 72: What is the cosine function definition in a right triangle?

Answer: $\text{cos}(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$. Cosine relates the side adjacent to the angle with the hypotenuse.

Flashcard 73: Find the longer leg in a 30-60-90 triangle with shorter leg $3$.

Answer: $3\text{√}3$. Longer leg equals shorter leg times $\sqrt{3}$.

Flashcard 74: What is the value of $\text{cos } 0^\text{o}$?

Answer:

1. Cosine of 0 degrees equals 1.

Flashcard 75: Calculate the hypotenuse: $a = 9$, $b = 12$.

Answer: $c = 15$. Using $9^2 + 12^2 = 81 + 144 = 225$.

Flashcard 76: Find side $a$ if $b = 6$, $c = 10$ in a right triangle.

Answer: $a = 8$. Using $a^2 + 6^2 = 10^2$, so $a^2 = 64$.

Flashcard 77: What is the area formula for a right triangle with base $b$ and height $h$?

Answer: $\frac{1}{2} \times b \times h$. Standard area formula for triangles using base and height.

Flashcard 78: What is the tangent of angle $A$ in a right triangle?

Answer: $\frac{\text{opposite}}{\text{adjacent}}$. Ratio of opposite side to adjacent side.

Flashcard 79: Find the length of the hypotenuse if legs are 6 and 8.

Answer:

1. Apply Pythagorean theorem: $\sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10$.

Flashcard 80: Which trigonometric function is equal to $\frac{1}{\text{sin } A}$?

Answer: Cosecant. Reciprocal trigonometric function of sine.

Flashcard 81: Find the length of the hypotenuse: $a = 3$, $b = 4$.

Answer: $c = 5$. Using $3^2 + 4^2 = 9 + 16 = 25$, so $c = 5$.

Flashcard 82: Find the other side if one leg is $5$ in a 45-45-90 triangle.

Answer: $5$. Both legs are equal in isosceles right triangle.

Flashcard 83: Which trigonometric function is equal to $\frac{1}{\text{cos } A}$?

Answer: Secant. Reciprocal trigonometric function of cosine.

Flashcard 84: What is the value of $\text{tan } 45^\text{o}$?

Answer:

1. Tangent equals 1 when opposite equals adjacent.

Flashcard 85: What is the value of $\text{cos } 0^\text{o}$?

Answer:

1. Cosine of 0 degrees equals 1.

Flashcard 86: What is the Pythagorean Theorem formula for a right triangle?

Answer: $a^2 + b^2 = c^2$. The fundamental relationship between the three sides of a right triangle.

Flashcard 87: What is the value of $\text{cos } 60^\text{o}$?

Answer: $\frac{1}{2}$. Standard trigonometric value for 60-degree angle.

Flashcard 88: Find the hypotenuse if each leg is $7$ in a 45-45-90 triangle.

Answer: $7\text{√}2$. Hypotenuse equals leg times $\sqrt{2}$ in 45-45-90 triangle.

Flashcard 89: Find the missing side: $b = 8$, $c = 10$ in a right triangle.

Answer: $a = 6$. Using $a^2 + 8^2 = 10^2$, so $a^2 = 36$.

Flashcard 90: What is the reciprocal of $\text{sin } A$?

Answer: Cosecant. Cosecant is the reciprocal of sine function.