Using the Pythagorean Theorem (Exact Answers)
Solve for a a2+102=202
a=10√ 3
Simplify √ 98
7 √ 2
The three sides of 14, 15, and 28 form a triangle.
True
14+15>28
Is this a right triangle?
3, 4, 5
Yes
A ladder is placed against a 10 ft. tall wall. The ladder is 24 ft. away from the wall. How long is the ladder? Round to the nearest tenth, if necessary.
26 ft.
Solve for b 22+b2=82
b=2√ 15
Simplify √ 18
3 √ 2
The side lengths 3, 4, 7 form a triangle
False
3+4 is not greater than 7
Is this a right triangle? Why?
6, 8, 10
Yes, because 62+82=102.
How far is the ladder from the base of a building if the building is 20 feet high and the ladder is 30 feet long? Round to the nearest tenth, if necessary.
22.4 Feet
Solve for c 122+152=c2
c=3√ 41
Simplify √ 32
4 √ 2
The side lengths 10, 10, 10 form a triangle
True.
Is this a right triangle?
23, 24, 25
No
A piece of cardboard was leaned against an 84 in. tall mirror. The cardboard is 13 in. away from the mirror. How long is the cardboard? Round to the nearest tenth, if necessary.
85 in.
Find the missing leg of a right triangle with side length of 4 and a hypotenuse of 16.
b=4√ 15
Simplify the square root of 108
6√ 3
A Pythagorean Triple is three positive integers that make a right triangle using the formula a2+b2=c2.
True.
Is this a right triangle?
33, 65, 234
No
What is the length of a skateboarding ramp if it is 12 feet long horizontally and 2 feet off the ground? Round to the nearest tenth, if necessary.
12.2 Feet
Find the hypotenuse of a right triangle with legs of 4 and 8
4√ 5
Simplify √ 450
15 √ 2
A triangle with side lengths 10, 23, and 25 is obtuse
False.
Is this a right triangle?
35, 613, 612
Yes
Richard jr.'s son put a 60 in. ladder up against a wall. If the ladder is 20 inches from the wall, how far up the wall does the ladder reach? Round to the nearest tenth, if necessary.
56.6 in.