Posted by **trigofunctions** on Tuesday, August 3, 2010 at 6:28am.

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?

- trigo -
**Henry**, Wednesday, August 4, 2010 at 8:26pm
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

- trigo -
**Henry**, Wednesday, August 4, 2010 at 8:42pm
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.

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