Question

Use the theorem below to answer the question. Suppose θ is an acute angle residing in a right triangle. If the length of the side adjacent to θ is a, the length of the side opposite θ is b, and the length of the hypotenuse is c, then cos(θ) = a c and sin(θ) = b c . If θ = 13° and the side adjacent to θ has length 4, how long is the hypotenuse? (Round your answer to three decimal places.)

Answer 1

Solve the equation where the sine of 30 degrees is equal to YZ/50.

Solve 180 – (30 + 90) = 60 to find the measure of angle Z. Then use the cosine of Z to write and solve an equation.

Use the 30°-60°-90° triangle theorem to find that YZ = 50/2.

Explanation:

These are the sample answers, use how you would like :)

Answer 2

c ≈ 4.105

Explanation:

You want to find c in ...

cos(13°) = 4/c

Multiply the equation by c/cos(13°) and evaluate.

c = 4/cos(13°) ≈ 4.105