Question

Points A and B are on the same horizontal line from the foot of a hill and the angles of depression of these points from the top of the hill are 30deg and 22deg, respectively. If the distance between A and B is 75m, what is the height of the hill?

Answer 1

The 2 lines of sight represent the
hypotenuse of 2 rt. triangles, and
the height of the hill represents the vertical side of both triangles. The
hor. side of smaller triangle(d) is
measured from the bottom of hill to A.
The hor. side of the larger triangle
is = to d + 75m.

Tan30 = h/d, h = d * Tan30.
h = (d+ 75)* Tan22

Answer 2

The 2 lines of sight represent the
hypotenuse of 2 rt. triangles, and
the height of the hill represents the vertical side of both triangles. The
hor. side of smaller triangle(d) is
measured from the bottom of hill to A.
The hor. side of the larger triangle
is = to d + 75m.

Tan30 = h/d,
h = d * Tan30.
h = (d + 75)* Tan22
Substitute d * Tan30 for h.
d * Tan30 = (d + 75) * Tan22.
Solve for d:
0.5774d = (0.4040d + 30.30.
0.5774d - 0.4040d = 30.30
0.1774d = 30.30.
d = 30.30/0.1774 = 174.74m.
h = 174.74 * Tan30 = 100.9m = height
of hill.

Answer 3

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