The length of shadow of a pole 50 m high is `(50)/(sqrt(3))` m. find the sun's altitude.

Answer

To find the sun's altitude given the height of the pole and the length of its shadow, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Height of the pole (AB) = 50 m
- Length of the shadow (BC) = \( \frac{50}{\sqrt{3}} \) m

2. **Draw a Right Triangle:**
- Let A be the top of the pole, B be the base of the pole, and C be the tip of the shadow on the ground.
- The triangle ABC is a right triangle where:
- AB is the height of the pole (perpendicular),
- BC is the length of the shadow (base),
- AC is the line of sight from the top of the pole to the tip of the shadow.

3. **Use the Tangent Function:**
- The angle of elevation (θ) from point B (the base of the pole) to point A (the top of the pole) can be calculated using the tangent function:
\[ \tan(θ) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{AB}{BC} \]
- Substituting the known values:
\[ \tan(θ) = \frac{50}{\frac{50}{\sqrt{3}}} \]

4. **Simplify the Expression:**
- Simplifying the right-hand side:
\[ \tan(θ) = 50 \times \frac{\sqrt{3}}{50} = \sqrt{3} \]

5. **Determine the Angle:**
- We know that \( \tan(60^\circ) = \sqrt{3} \).
- Therefore, \( θ = 60^\circ \).

6. **Conclusion:**
- The sun's altitude is \( 60^\circ \).

### Final Answer:
The sun's altitude is \( 60^\circ \).

---