Asked by Marie

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.
Answered by Reiny
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
= ....
Answered by Greg
y=92.5
x=157.9
x+y=250.4ft
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