A tunnel for a new highway is to be cut through a mountain that is 260 feet high. At a distance of 200 feet from the base of the mountain, the angle of elevation is 36 degrees. From a distance of 150 feet on the other side of the mountain, the angle of elevation is 47 degrees. Approximate the length of the tunnel to the nearest foot.

Question

Reiny · Answer

I drew triangle ABC where BC is a horizontal (the road) and angle B is 36° , and is on the left side of the diagram.
Angle C = 47° , on the right side
D is on BC and is the altitude of the mountain of 260 feet
I let BD = 200+x , and DC = 150+y

in the left triangle,
tan 36° = 260/(200+x)
200+x = 260/tan 36
x = 260/tan36 - 200 = 157.86 feet

find y in the same way.....

length of tunnel = x+y
= ....

Greg · Answer

y=92.5 x=157.9 x+y=250.4ft