Question

Use the image to answer the question.

A right triangle shows the hypotenuse labeled c, a leg labeled a, and a leg labeled b. The sides a and c form an angle phi, the sides a and b form a right angle, and the sides c and b form an angle theta.

If a=6 in.
and θ=45°
, find the value of c. Round your answer to the nearest hundredth.

(1 point)

Answer 1

Theta is the angle opposite side a, so sin θ = opposite/hypotenuse = a/c. Thus

c = a / sin θ = 6 / sin 45° = 6 / (√2/2) = 6√2 ≈ 8.49 in.

Answer: 8.49 in.