Question
Download Solution PDFTwo girls are standing on either side of a tower. The angles of depression from the top of the tower are observed to be 30° and 45° at the points on the ground where the two girls are standing. If the height of the tower is 18m, then find the distance between the girls. (Note: √3 = 1.7)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Height of the tower = 18 m
Angle of depression to first girl = 30°
Angle of depression to second girl = 45°
Use right triangle trigonometry: tan(θ) = height / distance
Formula used:
Distance = height ÷ tan(θ)
Calculations:
Let d₁ = distance of girl at 30° = 18 ÷ tan(30°) = 18 ÷ (1/√3) = 18 × √3 = 18 × 1.7 = 30.6 m
Let d₂ = distance of girl at 45° = 18 ÷ tan(45°) = 18 ÷ 1 = 18 m
Distance between the girls = d₁ + d₂ = 30.6 + 18 = 48.6 m
∴ Distance between the two girls = 48.6 meters
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