The-angle-of-elevation-of-the-top-of-a-building-24-m-high-is-observed-from-the-top-and-from-the-bottom-of-a-vertical-ladder-and-found-to-be-45-and-60-respectively-Find-the-height-of-the-ladder-

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Question Number 217424 by peter frank last updated on 13/Mar/25

The angle of elevation of the top of a building 24 m high is observed from the top and from the bottom of a vertical ladder, and found to be 45° and 60° respectively. Find the height of the ladder.

Answered by mr W last updated on 13/Mar/25

Commented by mr W last updated on 13/Mar/25

tan 60°=((24)/d)=(√3) d=((24)/( (√3)))=8(√3) 24−L=d tan 45°=d=8(√3) ⇒L=24−8(√3)≈10.14 m

$$\mathrm{tan}\:\mathrm{60}°=\frac{\mathrm{24}}{{d}}=\sqrt{\mathrm{3}} \\ $$$${d}=\frac{\mathrm{24}}{\:\sqrt{\mathrm{3}}}=\mathrm{8}\sqrt{\mathrm{3}} \\ $$$$\mathrm{24}−{L}={d}\:\mathrm{tan}\:\mathrm{45}°={d}=\mathrm{8}\sqrt{\mathrm{3}} \\ $$$$\Rightarrow{L}=\mathrm{24}−\mathrm{8}\sqrt{\mathrm{3}}\approx\mathrm{10}.\mathrm{14}\:{m} \\ $$

Commented by peter frank last updated on 14/Mar/25