From a window 9 meters from the ground, the angles of epression of the top and bottom of a lamp post..........

Question

From a window 9 meters from the ground, the angles of epression of the top and bottom of a lamp post are 30 degrees and 60 degrees, respectively.Find the height of the lamp post

the angles of *depression

Answer 1

The height is 9 meters plus the amount the top of the lamppost is above the window.

Let
A = window
T = top of lamppost
B = bottom of lamppost
C = point at which horizontal line from A intersects TB
D = base of building below window
_________

Triangle TAB is a right triangle with the right angle at A.
Angle TAC = 30°
Angle BAC = 60°

Triangles TAB, ACB, and BDA are all similar right triangles.

Angle
CB = 9

AC = BC/√3 = 9/√3

TC = AC/√3 = (9/√3)/√3 = 9/3 = 3

BT = BC + CT = 9 + 3 = 12

The height of the lamppost is 12 meters.

Answer 2

just use the law of sines a bunch of times
turns out to be 6

Answer 3

please define epression because i can't find it in the dictionary!!!