Geometry

Trigonometry

Medium

Two men are on opposite side of tower. They measure the angles of elevation of the top of the tower as 30° and 45° respectively. If the height of the tower is 50 meters, find the distance between the two men.

136.6 m

136 m

27.3 m

54.6 m

✅ Correct Option: 1

A tower has two men standing on opposite sides. The height of the tower is 50 meters. Man 1 measures an angle of elevation of 30° to the top, and Man 2 measures an angle of elevation of 45°.

Let $d_1$ be the distance from Man 1 to the base of the tower, and $d_2$ be the distance from Man 2 to the base of the tower.

For Man 2 with angle of elevation 45°:

$\tan(45°) = \dfrac{50}{d_2}$

Since $\tan(45°) = 1$ :

$1 = \dfrac{50}{d_2}$

$d_2 = 50$ m

For Man 1 with angle of elevation 30°:

$\tan(30°) = \dfrac{50}{d_1}$

Since $\tan(30°) = \dfrac{1}{\sqrt{3}}$ :

$\dfrac{1}{\sqrt{3}} = \dfrac{50}{d_1}$

$d_1 = 50\sqrt{3}$

$d_1 = 50 \times 1.732$

$d_1 = 86.6$ m

Since the men are on opposite sides of the tower, the total distance between them is:

Total Distance $= d_1 + d_2$

Total Distance $= 86.6 + 50$

Total Distance $= 136.6$ m

Therefore, the distance between the two men is 136.6 meters.

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Two men are on opposite side of tower. They measure the angles of elevation of the top of the tower as 30° and 45° respectively. If the height of the tower is 50 meters, find the distance between the two men.

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