Trigonometry Right Triangle Solutions 3

Question 1

In a right triangle with a 45° angle, if the hypotenuse is 10, what are the lengths of the two legs?

Accepted Answer

5√2 each

Answer

A 45-45-90 triangle has legs = hypotenuse/√2 = 10/√2 = 5√2.

Question 2

Right triangle XYZ has the right angle at Z. If XY = 17 and YZ = 15, what is tan X?

Accepted Answer

15/8

Answer

XZ = √(17² − 15²) = √(289 − 225) = √64 = 8; tan X = opposite/adjacent = YZ/XZ = 15/8.

Question 3

An observer stands 50 m from a building and looks up at a 38° angle of elevation to the top. What is the approximate height of the building?

Accepted Answer

50 tan 38°

Answer

The height = adjacent × tan(angle) = 50 tan 38°.

Question 4

In a 30-60-90 triangle, the side opposite the 60° angle is 6√3. What is the hypotenuse?

Accepted Answer

12

Answer

The side opposite 60° is (√3/2) × hypotenuse, so hypotenuse = 6√3 / (√3/2) = 12.

Question 5

If cos θ = 5/13 in a right triangle, what is tan θ?

Accepted Answer

12/5

Answer

With adjacent = 5 and hypotenuse = 13, opposite = 12 (Pythagorean triple), so tan θ = 12/5.

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