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