Mathematics

From the top of a 80 m high tower, the angles of depression of two men, on either sides of the tower, are found to be 32° and 58°. Find the distance between the two men correct to the nearest whole numbers.

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Let AB be the tower and C and D be the position of two different men.

From figure,

⇒ ∠ACB = ∠EAC = 32° (Alternate angles are equal)

⇒ ∠ADB = ∠FAD = 58° (Alternate angles are equal)

In △ ABD,

⇒ tan 58° = $\dfrac{AB}{BD}$

⇒ 1.6003 = $\dfrac{80}{BD}$

⇒ BD = $\dfrac{80}{1.6003}$ = 49.99 ≈ 50 m.

In △ ABC,

⇒ tan 32° = $\dfrac{AB}{BC}$

⇒ 0.6249 = $\dfrac{80}{BC}$

⇒ BC = $\dfrac{80}{0.6249}$ = 128.06 ≈ 128 m.

From figure,

CD = BC + BD = 128 + 50 = 178 m.

Hence, distance between two men = 178 m.

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