Question

A tree casts a shadow. If the tree is 34 feet tall, and the distance from the top of the tree to the top of the shadow is 47 feet, what is the angle formed from the top of the tree? Round your answer to the nearest whole degree.

The angle is approximately ___ degree.

Answer 1

To find the angle formed from the top of the tree to the top of the shadow, we can use trigonometry. We will set up a right triangle where:

- The height of the tree (34 feet) represents the opposite side.
- The distance from the top of the tree to the top of the shadow (47 feet) represents the hypotenuse.

We want to determine the angle \( \theta \) at the top of the tree.

We can use the sine function, which is defined as:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

Plugging in the values:

\[
\sin(\theta) = \frac{34}{47}
\]

Next, we calculate \( \frac{34}{47} \):

\[
\frac{34}{47} \approx 0.7234
\]

Now we will use the inverse sine function (arcsin) to find \( \theta \):

\[
\theta = \arcsin(0.7234)
\]

Using a calculator:

\[
\theta \approx 46.5\text{ degrees}
\]

Rounding to the nearest whole degree:

\[
\theta \approx 47\text{ degrees}
\]

Thus, the angle formed from the top of the tree is approximately **47 degrees**.