Because of prevailing winds, a tree grew so that it was leaning 6° from the vertical.At a point 43 meters from the tree, the angle of elevation to the top of the tree is 30° (see figure).Find the height a of the tree. c = 43 m
B = 96°

(Round your answer to two decimal places.)

A)24.58 m
B)26.58 m
C)25.58 m
D)28.58 m
E)27.58 m

Question

Because of prevailing winds, a tree grew so that it was leaning 6° from the vertical.At a point 43 meters from the tree, the angle of elevation to the top of the tree is 30° (see figure).Find the height a of the tree. ​  ​c = 43 m
B = 96°
​
(Round your answer to two decimal places.)
​
A)24.58 m 
B)26.58 m 
C)25.58 m 
D)28.58 m 
E)27.58 m

Quizplus · Accepted Answer

First, we need to find the angle at the top of the tree (angle A in the diagram). Using trigonometry:

tan(A) = opposite/adjacent 
tan(A) = h/43 
h = 43tan(A)

We can find angle A using the fact that the tree is leaning 6° from the vertical (angle B in the diagram) and the angle of elevation from 43 meters away is 30°.

tan(B) = opposite/adjacent 
tan(B) = x/43 
x = 43tan(B)

The height of the tree can be expressed as:

h = xtan(A+6)

Substituting the values we know:

h = (43tan(B))tan(30+6) 
h ≈ 26.58 meters

Therefore, the answer is choice B, 26.58 m.

Because of Prevailing Winds, a Tree Grew So That It