Properties of Right Triangles - SAT Math

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

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

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

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

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

1. Sine of 90 degrees equals 1.

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

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

Secant. Reciprocal trigonometric function of cosine.

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

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

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

Secant. Secant is the reciprocal of cosine function.

Cotangent. Reciprocal trigonometric function of tangent.

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

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

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

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

90 degrees. Right angle is always opposite the hypotenuse.

Cotangent. Cotangent is the reciprocal of tangent function.

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

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

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

1. Cosine of 0 degrees equals 1.

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

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

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

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

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

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

Pythagorean Theorem. Fundamental relationship between sides in right triangles.

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

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

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

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

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

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

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

1. Tangent equals 1 when opposite equals adjacent.

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

Cosecant. Cosecant is the reciprocal of sine function.

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

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

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

Cosecant. Reciprocal trigonometric function of sine.

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

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

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

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

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

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

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

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

Cosecant. Cosecant is the reciprocal of sine function.

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

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

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

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

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

1. Sine of 90 degrees equals 1.

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

Pythagorean Theorem. Fundamental relationship between sides in right triangles.

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

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

Secant. Reciprocal trigonometric function of cosine.

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

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

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

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

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

1. Cosine of 0 degrees equals 1.

Cotangent. Reciprocal trigonometric function of tangent.

90 degrees. Right angle is always opposite the hypotenuse.

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

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

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

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

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

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

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

Cotangent. Cotangent is the reciprocal of tangent function.

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

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

1. Tangent equals 1 when opposite equals adjacent.

Cosecant. Reciprocal trigonometric function of sine.

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

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

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

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

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

Secant. Secant is the reciprocal of cosine function.

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