trig word problems helps please?

Question

1) A surveyor measures the top of a building 50 ft away from him. His angle-measuring device is 4 ft above ground. The angle of elevation to the top of the building is 63 degrees. How fall is the building?

2) A forest ranger looking out from a ranger's station can see a forest fire at a 35 degree angle of depression. The ranger's position is 100 ft above the ground. How far is it from the ranger's station to the fire?

3) Let x and y be the measure of the acute angles of a right triangle. Explain why tan x degrees =1/ tan y degrees.

Answer 1

1. (h-4)/50 = tan 63°

h-4 = 50 tan 63 = 98.13

h = 102.13 ft



2. 100/d = tan 35

d = 100 / tan 35 = 142.8 ft



3. let the right angle be Z

tan x = YZ/XZ

tan y = XZ/YZ

so tan x and tan y are reciprocals, tan x = 1 / tan y = cot y



just as sin x = cos(90 - x), tan x = cot(90-x)

"cofunctions of complements are equal"

Answer 2

SOHCAHTOA! :D

1)

tan63 = x / 50

50tan63 = x = 8.49

then you need to add the 4 feet from before

8.48 + 4 = 12.49

2)

tan35 = x / 100

100tan35 = x = 47.38

3)

i'm sorry, but i don't know how to do this one... :(



hope i helped with the other two though x

Answer 3

(50ft tan63º) + 4 ft.



100ft / tan35º.