Question

A 30 foot tree casts a 12 foot shadow. Find the measure of the angle of elevation of the sun to the nearest degree

Answer 1

Drawing a right triangle, we know that the height of the tree is 30 and the length is 12. Trying to find the angle of the sun, we can say that the sun is the point where the hypotenuse and the height meet. Using tangent inverse, we have arctan(12/30) ≈ 21.8°

Answer 2

By using trigonometric relations, we will see that the angle of elevation of the sun is 68°.

How to find the angle of elevation of the sun?

Think of this as a right triangle, where te shadow and the height of the tree are the catheti.

The adjacent cathetus to the elevation of the sun, would be the length of the shadow.

Then we use the trigonometric relation:

Tan(a) = (opposite cathetus)/(adjacent cathetus)

And we get:

tan(a) = 30ft/12ft

Using the inverse tangent function in both sides we get:

a = Atan(30ft/12ft)  = 68°

The angle of elevation of the sun is 68°

If you want to learn more about right triangles, you can read:

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