### All SAT Math Resources

## Example Questions

### Example Question #1 : Apply The Pythagorean Theorem To Find The Distance Between Two Points In A Coordinate System: Ccss.Math.Content.8.G.B.8

Angela drives 30 miles north and then 40 miles east. How far is she from where she began?

**Possible Answers:**

60 miles

50 miles

35 miles

45 miles

**Correct answer:**

50 miles

By drawing Angela’s route, we can connect her end point and her start point with a straight line and will then have a right triangle. The Pythagorean theorem can be used to solve for how far she is from the starting point: a^{2}+b^{2}=c^{2}, 30^{2}+40^{2}=c^{2}, c=50. It can also be noted that Angela’s route represents a multiple of the 3-4-5 Pythagorean triple.

### Example Question #61 : Plane Geometry

To get from his house to the hardware store, Bob must drive 3 miles to the east and then 4 miles to the north. If Bob was able to drive along a straight line directly connecting his house to the store, how far would he have to travel then?

**Possible Answers:**

**Correct answer:**5 miles

Since east and north directions are perpendicular, the possible routes Bob can take can be represented by a right triangle with sides *a *and *b *of length 3 miles and 5 miles, respectively. The hypotenuse *c *represents the straight line connecting his house to the store, and its length can be found using the Pythagorean theorem: *c*^{2} = 3^{2}+ 4^{2} = 25. Since the square root of 25 is 5, the length of the hypotenuse is 5 miles.

### Example Question #2 : Apply The Pythagorean Theorem To Find The Distance Between Two Points In A Coordinate System: Ccss.Math.Content.8.G.B.8

A park is designed to fit within the confines of a triangular lot in the middle of a city. The side that borders Elm street is 15 feet long. The side that borders Broad street is 23 feet long. Elm street and Broad street meet at a right angle. The third side of the park borders Popeye street, what is the length of the side of the park that borders Popeye street?

**Possible Answers:**

16.05 feet

17.44 feet

18.5 feet

22.5 feet

27.46 feet

**Correct answer:**

27.46 feet

This question requires the use of Pythagorean Theorem. We are given the length of two sides of a triangle and asked to find the third. We are told that the two sides we are given meet at a right angle, this means that the missing side is the hypotenuse. So we use a^{2 }+ b^{2 }= c^{2}, plugging in the two known lengths for a and b. This yields an answer of 27.46 feet.

### Example Question #11 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle has legs of 15m and 20m. What is the length of the hypotenuse?

**Possible Answers:**

45m

30m

25m

40m

35m

**Correct answer:**

25m

The Pythagorean theorem is a^{2} + b^{2} = c^{2}, where a and b are legs of the right triangle, and c is the hypotenuse.

(15)^{2} + (20)^{2} = c^{2} so c^{2} = 625. Take the square root to get c = 25m

### Example Question #11 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Paul leaves his home and jogs 3 miles due north and 4 miles due west. If Paul could walk a straight line from his current position back to his house, how far, in miles, is Paul from home?

**Possible Answers:**

7

√14

4

25

5

**Correct answer:**

5

By using the Pythagorean Theorem, we can solve for the distance “as the crow flies” from Paul to his home:

3^{2} + 4^{2} = *x*^{2}

9 + 16 = *x*^{2}

25 = *x*^{2}

5 = *x*

### Example Question #101 : Plane Geometry

Given a right triangle where the two legs have lengths of 3 and 4 respectively, what is the length of the hypotenuse?

**Possible Answers:**

5

9

3

25

4

**Correct answer:**

5

The hypotenuse can be found using Pythagorean Theorem, which is a^{2 }+ b^{2 }= c^{2}, so we plug in a = 3 and b = 4 to get c.

c^{2 }=25, so c = 5

### Example Question #41 : Right Triangles

Length *AB* = 4

Length *BC* = 3

If a similar triangle has a hypotenuse length of 25, what are the lengths of its two legs?

**Possible Answers:**

5 and 25

20 and 25

3 and 4

15 and 25

15 and 20

**Correct answer:**

15 and 20

Similar triangles are in proportion.

Use Pythagorean Theorem to solve for *AC*:

Pythagorean Theorem: *AB*^{2} + *BC*^{2} = *AC*^{2}

4^{2} + 3^{2} = *AC*^{2}

16 + 9 = *AC*^{2}

25 = *AC*^{2}

*AC* = 5

If the similar triangle's hypotenuse is 25, then the proportion of the sides is *AC*/25 or 5/25 or 1/5.

Two legs then are 5 times longer than *AB* or *BC*:

5 * (*AB*) = 5 * (4) = 20

5 * (*BC*) = 5 * (3) = 15

### Example Question #21 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

If the base of a right triangle is 5 cm long and the height of the triangle is 7 cm longer than the base, what is the length of the third side of the triangle in cm?

**Possible Answers:**

**Correct answer:**

Find the height of the triangle

Use the Pythagorean Theorem to solve for the length of the third side, or hypotenuse.

### Example Question #21 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Given the right triangle in the diagram, what is the length of the hypotenuse?

**Possible Answers:**

**Correct answer:**

To find the length of the hypotenuse use the Pythagorean Theorem:

Where and are the legs of the triangle, and is the hypotenuse.

The hypotenuse is 10 inches long.

### Example Question #44 : Right Triangles

Triangle ABC is a right triangle. If the length of side A = 3 inches and C = 5 inches, what is the length of side B?

**Possible Answers:**

1/2 inches

1 inches

4 inches

6 inches

4.5 inches

**Correct answer:**

4 inches

Using the Pythagorean Theorem, we know that .

This gives:

Subtracting 9 from both sides of the equation gives:

inches

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