A forest Ranger spots a fire from a 28 foot tower. The angle of depression from the tower to the fire is 11°.
To the nearest foot, how far is the fire from the base of the tower? Show the steps you used to find the solution.

Question

A forest Ranger spots a fire from a 28 foot tower. The angle of depression from the tower to the fire is 11°. 
To the nearest foot, how far is the fire from the base of the tower? Show the steps you used to find the solution.

lilthesis101 · Answer

@undeadknight26

lilthesis101 · Answer

@ganeshie8

oleg3321 · Answer

Now, since the angle of depression is 11°, we can know the angle inside the triangle is 79°, since 11+79=90 (Forms right angle). 
Now, since a right angle is 90°, and since all angles in a triangle sums up to 180° (Triangle Angle Sum Theorem), the angle of elevation is 11°. 
Now we can use the Law of Sines to find the answer ("x" is the side we are looking for). 
x/sin(90) = 28/ sin(11)
x = (28/sin(11))sin(90) 
And, using a calculator:
x= 147 (rounded to the nearest foot)
So the distance between the tower and the fire is 147 feet. Hope this helps!

jim_thompson5910 · Answer

|dw:1468901808451:dw|
T = top of tower
B = base of tower
F = location of fire


use the trig function tangent to solve for x
tan(11 degrees) = 28/x