Question

MODELING WITH MATHEMATICS Scientists can measure the depths of craters on the moon by looking at photos ofshadows. The length of the shadow cast by the edge of a crater is 500 meters. The angle of elevation of the rays of the Sun is55°. Estimate the depth d of the crater to the nearest tenth.Sun's ray

Answer 1

714.1 m

Explanation:

The first thing is to make a sketch of the situation:

We can determine the value of the depth (d) by means of the tangent trigonometric function, like this:

`\begin{gathered} \tan\theta=\frac{\text{ opposite}}{\text{ adjacent}} \\ \\ \text{ We replacing:} \\ \\ \tan55\degree=(d)/(500) \\ \\ d=\tan55\degree\cdot500 \\ \\ d=714.1\text{ m} \end{gathered}`

The depth is 714.1 m