Pythagorean Theorem
If the legs of a right triangle are 3 units and 4 units, what is the length of the hypotenuse?
5 units
If one leg of a 45-45-90 triangle is 5 units, what is the length of the hypotenuse?
5√2
What is the geometric mean of 5 and 20?
10
A student is standing 10 feet away from a flagpole. The flagpole is 20 feet tall. If the angle of elevation from the student to the flag is 63.4 degrees, what is tangent of 63.4 degrees?
2
If sine of 77 degrees is 0.97, what is sine inverse of 0.97?
77 degrees
One example of a Pythagorean Triple is the sides 5, 12, and 13. Name three other triples that would form a right triangle.
3, 4, 5
6, 8, 10
10, 24, 26
If the short leg of a 30-60-90 triangle is 4 units, what is the length of the hypotenuse? What is the length of the long leg?
8 and 4√3
The altitude of a right triangle splits the hypotenuse into two segments. One is 8 units and one is 2 units. How long is the altitude?
4 units
A right triangle has an acute angle of 35 degrees. If the leg adjacent to the angle is 12 units long, how long is the leg opposite the angle? (Use a calculator!)
8.4 units
A 15 foot ladder is leaned against a house. The base of the ladder is 4 feet from the house. How would you use inverse trig to find the angle of elevation of the ladder?
Cosine inverse of 4/15
If one leg of a right triangle is 8 units and the hypotenuse is 17 units, what is the length of the other leg? (Use a calculator!)
15 units
If the hypotenuse of a 30-60-90 triangle is 10√3, what are the lengths of the legs?
5√3 and 15
The altitude of a right triangle splits the hypotenuse into two segments. One is 4 units and one is 12 units. How long is the short leg?
8 units
A zipline is attached to the top of a 50 foot building. Your friend is at the top of the building about to go down the zipline, and you are at the bottom of the zipline, having just gone down. If the angle of elevation from you to your friend is 41.8 degrees, how long is the zipline? (Use a calculator!)
75 feet
if tangent inverse of 3/4 is approximately 37 degrees, what is tangent inverse of 4/3? (No calculators allowed!)
53 degrees