Question

Let ∠D be an acute angle such that sinD=0.75. Use a calculator to approximate the measure of ∠D to the nearest tenth of a degree.

What is the measure of
Please show all the work on how you got your answer.

Answer 1

If $\sin(D)=0.75$ then $\arcsin(0.75)=D\approx48.59^{\circ}$

Hope this helps.

Answer 2

For finding the measure of angle when a trigonometric ratio is given, we use inverse trigonometric functions.

The measure of ∠D is $\angle D \approx 48.59^{\circ}$

How to find the measure of angle D using trigonometric ratios?

For finding the measure of angle when a trigonometric ratio is given, we use inverse trigonometric functions.

For example, for sine there lies arcsin, for cos, there lies arccos and so on.

Thus,

$sin(D) = 0.75\\\angle D = arcsin(0.75) \in \{ 48.59, 131.409\}$

But since ∠D is acute, thus we have $\angle D \approx 48.59^{\circ}$

Thus, the measure of ∠D is  $\angle D \approx 48.59^{\circ}$

Learn more about inverse trigonometric ratio arcsin here:

https://brainly.com/question/1634690