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

Let's call the height of the tree "a". Since the tree is leaning 6° from the vertical and we know the distance from the tree to point C (43 meters), we can use the tangent function to find the horizontal distance from the tree to point C.

tan(6°) = x/43

x = 43tan(6°) ≈ 4.55

So, the horizontal distance from the tree to point C is approximately 4.55 meters.

Now we can use the tangent function again to find the height of the tree.

tan(30°) = a/(43 + 4.55)

a ≈ (43 + 4.55)tan(30°) ≈ 26.58 meters

Therefore, the height of the tree is approximately 26.58 meters, which corresponds to choice B.

Because of Prevailing Winds,a Tree Grew So That It Was