Question

When the altitude of the sum is 50°,Find the length of the shadow cast by a vertical pole of height 30m on the horizontal ground

Answer 1

To find the length of the shadow cast by a vertical pole due to the sun's altitude at 50°, we can use some basic trigonometry.

The situation can be represented in a right triangle where:
- The height of the pole is the opposite side (30 m).
- The length of the shadow is the adjacent side.
- The angle of elevation (altitude of the sun) is 50°.

Using the tangent function, which is the ratio of the opposite side to the adjacent side, we have:

\[
\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}
\]

In this case, it can be expressed as:

\[
\tan(50°) = \frac{30 \, \text{m}}{\text{length of shadow}}
\]

Let \( L \) be the length of the shadow:

\[
\tan(50°) = \frac{30}{L}
\]

Rearranging the equation to solve for \( L \):

\[
L = \frac{30}{\tan(50°)}
\]

Now, we need to calculate \( \tan(50°) \).

Using the value of \( \tan(50°) \):

\[
\tan(50°) \approx 1.1918
\]

Therefore:

\[
L = \frac{30}{1.1918} \approx 25.13 \text{ m}
\]

Thus, the length of the shadow cast by the vertical pole is approximately **25.13 meters**.