Question

A man who is 2 m tall stands on horizontal ground 30 m away from a tree. The angle of elevation of the top of the tree from his eyes is 28˚. Estimate the height of the tree.
(Use sin 28° = 0.4694, cos 28° = 0.8829, and tan 28° = 0.5371)

• A. 7.3 m
• B. 17.95 m
• C. 10.8 m
• D. 5.3 m

Answer 1

The correct option is B 17.95 m

Let the height of the tree be h.
The given diagram illustrates the situation mentioned in the question.


So, BD = h, and BC = (h-2)
Now,
$tan28°=\frac{BC}{AC}tan28°=\frac{(h-2)}{30}(h-2)=30\times tan28°(h-2)=30\times 0.5371=15.951h=15.951+2=17.951$

Hence, the height of tree is 17.95 m.