Question

What is the correct answer?
Lorenzo is 6 feet, 3 inches in height. He looks at his shadow when the angle of elevation of the sun is 35°.
What is the approximate length of his shadow?

Answer 1

To find the length of Lorenzo's shadow when the angle of elevation of the sun is 35°, we can use trigonometry.

Given that Lorenzo’s height is 6 feet 3 inches, we first convert this to feet:

- 3 inches = 3/12 feet = 0.25 feet
- Therefore, Lorenzo's height = \( 6 + 0.25 = 6.25 \) feet.

Let \( h \) be Lorenzo's height (6.25 feet) and \( L \) be the length of his shadow. The angle of elevation (θ) is 35°.

Using the tangent function which relates the height of an object to the length of its shadow and the angle of elevation:

\[
\tan(θ) = \frac{h}{L}
\]

We can rearrange this to find \( L \):

\[
L = \frac{h}{\tan(θ)}
\]

Substituting the values:

\[
L = \frac{6.25}{\tan(35°)}
\]

Now, we need to calculate \( \tan(35°) \). Using a calculator:

\[
\tan(35°) \approx 0.7002
\]

Now we can find the length of the shadow:

\[
L = \frac{6.25}{0.7002} \approx 8.93 \text{ feet}
\]

Thus, the approximate length of Lorenzo's shadow is about **8.93 feet**.