Posted by **Marie** on Tuesday, June 5, 2012 at 8:07pm.

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.

- trig -
**Reiny**, Tuesday, June 5, 2012 at 8:33pm
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

= ....

- trig -
**Greg**, Tuesday, October 16, 2012 at 6:51pm
y=92.5

x=157.9

x+y=250.4ft

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