Question

What is the measure of ∠D ?

Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.

Answer 1

The answer is 29.05

Explanation:

I just took the test.

Answer 2

Answer: The measure of ∠D is 29° approximately.

Step-by-step explanation: We are given a right-angled triangle BCD, where ∠C = 90°, BC = 25 ft and CD = 45 ft.

In ΔBCD, with respect to ∠D, we have

base, b = CD = 45 ft,

perpendicular, p = BC = 25 ft

and

hypotenuse, h = BD.

Therefore, we can write

`\tan \angle D=(p)/(b)\\\\\Rightarrow \tan \angle D=(25)/(45)\\\\\Rightarrow \tan \angle D=(5)/(9)\\\\\Rightarrow \tan \angle D=0.555...\\\\\Rightarrow \angle D=\tan^(-1)(0.555...)\\\\\Rightarrow \angle D\sim 0.506~\textup{radians}.`

Now,

`\pi~\textup{radians}=180^\circ,\\\\1~\textup{radian}=(180^\circ)/(\pi),\\\\0.506~\textup{radians}=(180^\circ* 0.506)/((22)/(7))=(180^\circ* 0.506* 7)/(22)=28.98^\circ\sim 29^\circ.`

Thus, the measure of ∠D is 29° approximately.