Question

The angle of elevation of the top a rock from the top and foot of a 100m high tower are 30 and 45 degree.Find the height of the rock.

Answer 1

The angle of elevation of the top a rock from the top and foot of a 100m high tower are 30 and 45 degree. Find the height of the rock.

$$h = 100\, \text{m}$$ $$H = h_1 + h = L \cdot \sin 45$$ $$h_1 = L \cdot \sin 30$$ $$L \cdot \sin 30 + h = L \cdot \sin 45$$ $$L = \frac{h}{\sin 45 - \sin 30}$$ $$H = L \cdot \sin 45 = \frac{h}{\sin 45 - \sin 30} \cdot \sin 45$$

Calculation

$$H = \frac{100}{\sin 45 - \sin 30} \cdot \sin 45 \approx 341.42\, \text{m}$$

Answer: 341.42 m