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.

## Answer this Question

## Related Questions

- trigonometric problem - Point A and B are on the same horizontal line with the ...
- Math help please - Which hill described in the table is the steepest? Explain. ...
- trigonometry - a tower 150 meter is situated at the top of the hill.At a point ...
- math - Street | Horizontal | Vertical rise Distance ft. |of street ft. _______|...
- physics - The cart starts from rest at the top of a hill with height, H2. It ...
- physics - The cart starts from rest at the top of a hill with height, H1. It ...
- math - Which hill described in the table is the steepest? (Table) Street: ...
- Math - Which hill described in the table is the steepest? (Table) Street: ...
- math help please - Which hill described in the table is the steepest and why? ...
- trig - A hill rises from the horizontal at 15º. The road leading straight up the...

More Related Questions