A 4 foot person casta a 7 foot shadow. Find the angle of elevation of the sun.

Answer 1

Hi Isabella!

This problem looks a little odd at first, but you can get a pretty good view of it by drawing a picture. I'll give it a shot here and we can see if it works :)

4 feet tall...

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|_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _> 7 foot shadow...

We're going to be looking to figure out what the angle at the bottom right of the triangle is - that'll be our angle of elevation. In order to do that, let's look at the two numbers given. We have the height of the person, which is opposite the angle, and the length of the shadow which is adjacent to the angle. Since the only trigonometric function that uses "opposite and adjacent" is tangent, we'll use the tangent to get the angle!

Tan (angle) = Opposite / Adjacent

Tan (angle) = 4/7

So from here, we take the arctangent (or tan^-1) of both sides...

Angle = tan^-1(4/7)

To give us an angle of elevation of....29.7 degrees!

Hope that helps!

-Niral