All High School Math Resources
Example Questions
Example Question #1 :How To Find The Length Of The Side Of A Right Triangle
A right triangle has one side equal to 5 and its hypotenuse equal to 14. Its third side is equal to:
12
171
9
13.07
14.87
13.07
The Pythagorean Theorem gives usa2+b2=c2for a right triangle, wherecis the hypotenuse andaandbare the smaller sides. Hereais equal to 5 andcis equal to 14, sob2= 142– 52= 171. Thereforebis equal to the square root of 171 or approximately 13.07.
Example Question #9 :How To Find The Length Of The Side Of A Right Triangle
Which of the following could NOT be the lengths of the sides of a right triangle?
12, 16, 20
5, 7, 10
5, 12, 13
8, 15, 17
14, 48, 50
5, 7, 10
We use the Pythagorean Theorem and we calculate that 25 + 49 is not equal to 100.
All of the other answer choices observe the theorema2+b2=c2
Example Question #2 :How To Find The Length Of The Side Of A Right Triangle
Which set of sides could make a right triangle?
4, 6, 9
6, 7, 8
10, 12, 16
9, 12, 15
9, 12, 15
By virtue of the Pythagorean Theorem, in a right triangle the sum of the squares of the smaller two sides equals the square of the largest side. Only 9, 12, and 15 fit this rule.
Example Question #1 :How To Find The Length Of The Side Of A Right Triangle
A right triangle with a base of 12 and hypotenuse of 15 is shown below. Find x.
5
5.5
4
4.5
3.5
4
Using the Pythagorean Theorem, the height of the right triangle is found to be = √(〖15〗2–〖12〗2) = 9, so x=9 – 5=4
Example Question #2 :How To Find The Length Of The Side Of A Right Triangle
A right triangle has sides of 36 and 39(hypotenuse). Find the length of the third side
33√2
42
15
12 √6
33
15
use the pythagorean theorem:
a2+ b2= c2; a and b are sides, c is the hypotenuse
a2+ 1296 = 1521
a2= 225
a = 15
Example Question #3 :How To Find The Length Of The Side Of A Right Triangle
Bob the Helicopter is at 30,000 ft. above sea level, and as viewed on a map his airport is 40,000 ft. away. If Bob travels in a straight line to his airport at 250 feet per second, how many minutes will it take him to arrive?
1 hour and 45 minutes
2 hours and 30 minutes
3 minutes and 50 seconds
3 minutes and 20 seconds
4 hours and 0 minutes
3 minutes and 20 seconds
Draw a right triangle with a height of 30,000 ft. and a base of 40,000 ft. The hypotenuse, or distance travelled, is then 50,000ft using the Pythagorean Theorem. Then dividing distance by speed will give us time, which is 200 seconds, or 3 minutes and 20 seconds.
Example Question #4 :How To Find The Length Of The Side Of A Right Triangle
A right triangle has two sides, 9 andx, and a hypotenuse of 15. What isx?
12
11
10
14
13
12
We can use the Pythagorean Theorem to solve forx.
92+x2= 152
81 +x2= 225
x2= 144
x= 12
Example Question #5 :How To Find The Length Of The Side Of A Right Triangle
The area of a right traingle is 42. One of the legs has a length of 12. What is the length of the other leg?
Example Question #141 :Plane Geometry
Ifand, what is the length of?
AB is the leg adjacent to Angle A and BC is the leg opposite Angle A.
Since we have atriangle, the opposites sides of those angles will be in the ratio.
Here, we know the side opposite the sixty degree angle. Thus, we can set that value equal to.
which also means
Example Question #6 :How To Find The Length Of The Side Of A Right Triangle
Solve forx.
2
7
12
6
6
Use the Pythagorean Theorem. Leta= 8 andc= 10 (because it is the hypotenuse)