A vertical pole of 10.7m stands on a level ground. If the sun's ray strike at an angle of 34°. Calculate the length of the shadow of the pole on the ground 

To calculate the length of the shadow of the pole, we can use trigonometry.

In this situation, the vertical pole, the shadow, and the line representing the sunlight form a right triangle. The pole is the opposite side to the angle of the sun's rays, and the shadow is the adjacent side. The tangent function relates the angle to the opposite and adjacent sides of a right triangle:

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

Here:
- \(\theta = 34^\circ\) (the angle of the sun’s rays),
- \(\text{opposite} = 10.7 \, \text{m}\) (the height of the pole),
- \(\text{adjacent} = \text{length of the shadow}\).

We can rearrange the formula to find the length of the shadow:

\[
\text{shadow length} = \frac{{\text{opposite}}}{{\tan(\theta)}} = \frac{10.7}{\tan(34^\circ)}
\]

Now, let's calculate it:

\[
\text{shadow length} = \frac{10.7}{\tan(34^\circ)} \approx \frac{10.7}{0.6745} \approx 15.86 \, \text{m}
\]

So, the length of the shadow is approximately **15.86 meters**.

Would you like more details on this? Here are 5 related questions:

1. What is the effect of changing the angle of the sun on the length of the shadow?
2. How do we calculate the angle of elevation if the shadow length and pole height are known?
3. What happens if the angle of the sun is 0°? What does it mean?
4. How can we calculate the angle of the sun if only the height of the pole and shadow length are known?
5. How does trigonometry apply in real-world situations like this one?

**Tip:** The tangent function is often useful in problems involving heights and shadows in right triangles!

A vertical pole of 10.7m stands on a level ground. If the sun's ray strike at an angle of 34°, calculate the length of the shadow of the pole on the ground.

Learn how to calculate the shadow length of a 10.7m vertical pole when the sun's rays strike at an angle of 34°. Using trigonometry and the tangent function, this problem demonstrates how to solve real-world problems involving right triangles. Suitable for students in Grades 9-11.

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