A surveyor stands at a point on level ground 50\text{ m} away from the base of a vertical … — JAMB UTME

A surveyor stands at a point on level ground $50\text{ m}$ away from the base of a vertical transmission tower. If the angle of elevation from the observer's position on the ground to the top of the tower is $45^\circ$ , what is the height of the tower in meters?

Answer: 50 meters

Answer

The height of the transmission tower is

50\text{ meters}

In a right-angled triangle, the tangent of the angle of elevation equals the ratio of the height (opposite side) to the horizontal distance (adjacent side). Since

\tan(45^\circ) = 1

, the height of the tower must be equal to the horizontal distance of

50\text{ m}

Step-by-Step Solution

Formulate the trigonometric relationship using the right triangle formed by the observer, the base of the tower, and the top of the tower.

\tan(45^\circ) = \frac{h}{50}

, where

h

is the height of the tower.

The tangent ratio relates the opposite side (height of tower) to the adjacent side (distance along level ground).

Substitute the value of

\tan(45^\circ) = 1

and solve for

h

h = 50 \times 1 = 50\text{ m}

Multiplying the adjacent side length by

\tan(45^\circ)

yields the exact height.

Key Concept

Angle of elevation using basic right-triangle trigonometry

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