Question

Scientists can estimate the depth of craters on the moon by studying the lengths of their shadows in the craters. Find the depth of a crater, if the shadow is estimated to be 400 m long and the angle of elevation of the sun is 48°.

Answer 1

It's a much more interesting problem when we have to estimate the shadow length from a photo.

The crater is a curvy bumpy surface, but let's approximate it as part of a sphere and just conflate the arc and chord length, so the 400 m shadow corresponds to a 400 m chord from the edge at the surface to the bottom.

The shadow as a chord forms a hypotenuse right triangle with the depth d being the leg opposite the 48 degree angle of the sun.

$d = 400 \sin 48 \approx 297 \textrm{  m}$

Answer: 297 m

Answer 2

The depth is 297.26 m.

Height and distance

It is the application of trigonometry.

Right angle triangle

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

Given

The shadow is estimated to be 400 m long.

And the angle of elevation of the sun is 48°.

To find

The depth of a crater.

How to get the depth of a crater?

Hypotenuse = 400m

Angle = 48°

The by the sine rule

$\begin{aligned} \rm sin \theta &= \rm \dfrac{Depth}{Hypotenuse}\\\\\rm sin 48^o &= \rm \dfrac{depth}{400}\\\\\rm depth &= \rm sin 48^o * 400\\\\\rm depth &= 297.2579 \approx 297.26 \end{aligned}$

Thus, the depth is 297.26 m.

More about the height and distance link is given below.

https://brainly.com/question/10681300