QuestionFind the angle of elevation of the sun when a 40 ft tree casts a 58 ft shadow.

Studdy Solution

STEP 1

Assumptions1. The tree is40 feet high. . The shadow cast by the tree is58 feet long.
3. We are assuming the tree, the end of the shadow, and the sun form a right triangle, with the angle of elevation being the angle between the tree and the line to the sun.

STEP 2

We can use the tangent of the angle of elevation to find the measure of the angle. The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
$\tan(\theta) = \frac{Opposite}{Adjacent}$

STEP 3

In this case, the length of the tree is the side opposite the angle, and the length of the shadow is the side adjacent to the angle. $\tan(\theta) = \frac{40}{58}$

STEP 4

To find the measure of the angle, we need to find the inverse tangent (or arctangent) of the ratio. $\theta = \arctan\left(\frac{40}{58}\right)$

STEP 5

Now we can calculate the angle of elevation.
$\theta = \arctan\left(\frac{40}{58}\right) \approx34.99^{\circ}$ The angle of elevation of the sun is approximately34.99 degrees.

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