Help me with this trigonometry/problem solving question.

Question

From an observation tower that overlooks a small lake, the angles of depression of point A, on one side of the lake, and point B, on the opposite side of the lake are, 7° and 13°, respectively, the points and the tower are in the same vertical plane and the distance from A to B is 1km. Determine the height of the tower.

Answer 1

α=6°

a=1km

a/sinα=b/sinβ=c/sinγ

1/.104=9.566=9.321/.974asin

β=77°

γ=97°

closest triangle=

α=7°

c=9.321 (side "b" above)

γ=90°

a/sinα=c=9.321

a/sin7°=9.321; a=1.136

c^2-a^2=b^2

86.881-1.29=85.59^.5=9.251................km

Answer 2

Using Law of Sines is also an option.

If h is the hypotenuse of the triangle with an acute angle of 13 degrees we can use the triangle with a side of 1 KM and angles of 7 and 6 degrees to reach: h/sin7 = 1/sin 6. That is, h = sin 7/sin 6.

Then from the right triangle with acute angle 13 degrees we have sin 13 = y/h. So the height of the tower can also be found as y = (sin7)(sin13)/(sin6)