Because of prevailing winds, a tree grew so that it was leaning 6º from the vertical. At a point d = 37 meters from the tree, the angle of elevation to the top of the trees is a = 29° (see figure). Find the height h of the tree. (Round your answer to one decimal place.)
h =
m
d m
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Height of the tree is 40.0 meters.

Step-by-step explanation:

From ΔABC,

m∠ABC = 90°

Since, m∠ABC = m∠CBD + m∠ABD

90° = 6° + m∠ABD

m∠ABD = 90°- 6° = 84°

By triangle sum theorem in ΔABD,

m∠ABD + m∠BDA + m∠DAB = 180°

84° + 29° + m∠BDA = 180°

m∠BDA = 180° - 113°

             = 67°

By sine rule in ΔABD,

h =

h = 39.98

h ≈ 40.0 meters

Therefore, height of the tree is 40.0 meters.

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