Question

You are traveling in a car toward a certain mountain at a speed of 80km/hr. The apparent size of the mountain is .5degrees. Fifteen minutes later the same mountain has an apparent size of 1 degree. About how tall is the mountain?

I believe you must convert the degrees to radians, but I am not sure what to do after that. If someone could at least get me started in the right direction, I would greatly appreciate it. Thanks

Answer 1

These are small angles, so the tangent of the small angle is the same as the angle in radians.

angle= angleindegrees(PI radians/180 deg)
= .5 (3.14/180)

Draw the system. The original distance is d

h/d=.5(3.14/180)
The next distance is 20km less, so
h/(d-20)=1.0 (3.14/180)

solve each equation for d

d= 2*180/3.14 h and
d= 180/3.14 h + 20

set these two equal, and solve for h.

check my thinking.

Answer 2

350 meters