From a certain distance from the base of a Giant Sequoia tree a surveyor determines that the angle of elevation to the top of the tree is 47deg. The surveyor then walks 100 feet away from the tree and determines that the angle of elevation to the top of the tree is now 37deg. How tall is the tree? You may assume that the ground is level.

Question

How exactly do I go about solving this and what is the correct answer so I can make sure I follow correctly?

Answer 1

as usual, draw a diagram. If the height is h, and the surveyor started out at a distance x from the tree,

h/x = tan47°
h/(x+100) = tan37°

equating the values for x,

h/tan47° = h/tan37° - 100
h/1.072 = h/.7535 - 100
h = 253.6 ft

Answer 2

Using law of sines, this is what I got:

x/sin37° = 100/sin10°
x = 346.6 ft

h/sin47° = 346.6/sin90°
h = 253.5 ft

Is this wrong...?

Answer 3

Nope. As usual, there is more than one way to do it. I picked my way to avoid actually having to find the value of x.

Answer 4

a building 60 feet high. from a distance at point A on the ground, the angle of elevation to the top of the building is 40 degree. from a little nearer at point B, the angle of elevation to the top of the building is 70 degree. What's the distance between point A and B?