Question

A shadow of a tower standing on a level ground is found to be 40√3 meters longer when the Sun's altitude is 30° than when it is 60°. The height of the tower is:

• A. 50 m
• B. 60 m
• C. 70 m
• D. 40 m

Answer 1

Answer:

B. 60 m

$tan60=\sqrt3=\frac hx$

$tan 30= \frac{1}{\sqrt3}=\frac{h}{40\sqrt3 +x}$

$x=\frac{h}{\sqrt3}$

$40\sqrt3+\frac{h}{\sqrt3}=\sqrt3h$

$120+h=3h$

$120=2h$

$h=60$