Question

A wire is fastened to a point T on a tree and to point A located 8.8 ft from the base of the tree along level ground (see figure). The angle

that the wire makes with level ground is 41°, and the tree leans 14° from vertical away from point A. How high off the ground is the point
where the wire is fastened to the tree? Round to the nearest tenth of a foot.
245

Answer 1

9.8 ft

Explanation:

You didn't post the figure, but I think I get the picture.

Find the acute angle (x) the tree makes with the ground:

90 + 14 + x = 180

x = 76

Complementary angle = 180 - 76 = 104

Angle formed by the tree and the wire = 180 - 104 - 41 = 35 (sum of interior angles of a triangle = 180)

Now you have all the angles needed to solve the problem.

Using law of sines to find the length of the tree (T) from the ground to point T:

sin41/T = sin35/8.8

T = 10.0655

Now find H, the vertical height from the ground to point T:

sin76 = H/10.0655

H = 9.7665 ≈ 9.8 ft