A man 1.7m tall observes a bird on top of a tree at an angle of 30^\circ. if the distance between the man's head and the bird is 25m, what is the height of the tree?
A
26.7m
B
14.2m
C
\(1.7+(25\frac{\sqrt{3}}{2}m\)
D
\(1.7+(25\frac{\sqrt{2}}{2}m\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Hint: Make a sketch forming a right angled triangle. Let x = height of the tree above the man. Such that x/25 = sin 30.
x = 12.5m
The height of the tree = 12.5 + 1.7
= 14.2 m
Source: Myschool Past Questions Archive (Record #27)