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-

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

$$\tan 60°=\frac{24}{d}=\sqrt{3}$$$$d=\frac{24}{\sqrt{3}}=8\sqrt{3}$$$$24-L=d\tan 45°=d=8\sqrt{3}$$$$\Rightarrow L=24-8\sqrt{3}\approx 10.14m$$

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

$$\mathrm{thank}\mathrm{you}$$

Answered by Spillover last updated on 13/Mar/25

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

$$\mathrm{thank}\mathrm{you}$$

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