Question

What is the measure of angle D?

Enter your answer as a decimal, round only your final answer to the nearest hundredth.

Answer 1

Answer: Angle D= 0.51 radians or 29.05°

Explanation:

For this problem, we can use our trigonometry to find the measure of angle D.

Since this is a right triangle, we know we can use sine, cosine, and tangent. We are focusing on angle D, so we would see which trigonometric function best fits angle D. Looking at where 25 ft and 45 ft are labeled, we can use tangent. Tangent of opposite/adjacent. Now that we know this, we can set up an equation. Let's use θ in place for angle D.

tan(θ)=25/45

tan(θ)=5/9

Since we want to find θ, we would do inverse tangent.

θ=
`tan^-^1((5)/(9) )`

θ=0.507

θ=0.51

This answer is in radians. In degrees, it is 29.05°.