Question

A tower is 60 m high. Its shadow is x metres shorter when the sun’s altitude is 45° instead of 30°. Then, x is equal to:

• A. 43 m
• B. 41.92 m
• C. 45.6 m
• D. 43.92 m

Answer 1

The correct option is D

43.92 m

$LetBDisxandDCisyIntriangleADC,Tan{45}^{\circ }=\frac{AC}{CD}1=\frac{60}{y}y=60mIntriangleABC,Tan{30}^{\circ }=\frac{AC}{BC}\frac{60}{x+y}=\frac{1}{\sqrt{3}}60+x=60\sqrt{3}x=60\sqrt{3}-60x=60\left(\sqrt{3}-1\right)=43.92mTheShadowwillbe43.92mshorter$