SAT Math : Plane Geometry

Study concepts, example questions & explanations for SAT Math

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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

Explanation:

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: a2+b2=c2, 302+402=c2, 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:
15 miles
9 miles
5 miles
7 miles
25 miles
Correct answer: 5 miles
Explanation:

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: c2 = 32+ 42 = 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

Explanation:

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+ b= c2, 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

Explanation:

The Pythagorean theorem is a2 + b2 = c2, where a and b are legs of the right triangle, and c is the hypotenuse.

(15)2 + (20)2 = c2 so c2 = 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

Explanation:

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

32 + 42 = x2

9 + 16 = x2

25 = x2

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

Explanation:

The hypotenuse can be found using Pythagorean Theorem, which is a+ b= c2, so we plug in a = 3 and b = 4 to get c.

c2  =25, so c = 5

Example Question #41 : Right Triangles

Triangle

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

Explanation:

Similar triangles are in proportion.

Use Pythagorean Theorem to solve for AC:

Pythagorean Theorem:  AB2 + BC2 = AC2

42 + 32 = AC2

16 + 9 = AC2

25 = AC2

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:

Explanation:

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

Screen_shot_2013-09-16_at_11.16.22_am

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

 

Possible Answers:

Correct answer:

Explanation:

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

Righttriangle

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

Explanation:

Using the Pythagorean Theorem, we know that .

This gives: 

Subtracting 9 from both sides of the equation gives: 

 inches

 

Righttriangle

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