CUET UG 2025 — General Test Geometry

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 $d_1$d1​ be the distance from Man 1 to the base of the tower, and $d_2$d2​ be the distance from Man 2 to the base of the tower.

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For Man 2 with angle of elevation 45°:

$$\tan(45°) = \dfrac{50}{d_2}$$tan(45°)=d2​50​

Since $\tan(45°) = 1$tan(45°)=1:

$$1 = \dfrac{50}{d_2}$$1=d2​50​

$d_2 = 50$d2​=50 m

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For Man 1 with angle of elevation 30°:

$$\tan(30°) = \dfrac{50}{d_1}$$tan(30°)=d1​50​

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

$$\dfrac{1}{\sqrt{3}} = \dfrac{50}{d_1}$$3​1​=d1​50​

$$d_1 = 50\sqrt{3}$$d1​=503​

$$d_1 = 50 \times 1.732$$d1​=50×1.732

$d_1 = 86.6$d1​=86.6 m

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

Total Distance $= d_1 + d_2$=d1​+d2​

Total Distance $= 86.6 + 50$=86.6+50

Total Distance $= 136.6$=136.6 m

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