Question

A tower 125 feet high stands on a side of ahill. Atapoint 240 feet from the foot of the tower, measuredstraight down the hill, the tower substends anangleof25 . What angle does the side of the hill makeswiththe horizontal?

Answer 1

Answer:

11°

Step-by-step explanation:

T = top of tower

B = base of tower

D = point 240' downhill

draw a right triangle with hypotenuse TD.

Let E be the right angle.  

From the law of sines,  

125/sin 25° = 240/sin ∠T

∠T is angle DTB

∠T = 54°

Now you have angle T, since

∠TDB + ∠BDE + ∠DTB = 90°

25° + ∠BDE + 54° = 90°  

∠BDE = 11° is the angle you want.