The apparent size of a mountain

Question

Peter travels in a car toward a certain mountain at the speed of 90km/h. The apparent size of the mountain is 1 degree. Twenty minutes later the same mountain has an apparent size of 1.8 degrees. About how tall is the mountain

Answer 1

Sketch a diagram. Don't worry if it's not to scale (it probably won't be).

Represent the initial distance to the mountain by x.

Figure out how closer Peter got to the mountain in 20 minutes (1/3 hour). 90*(1/3)=30

Now you have a new distance represented by x-30

Now you can set up two trig equations. One for the ratio of the height of the mountain over the initial distance (O/A) as expressed by tan 1. The second for the height over the new distance (tan 1.8).

With two equations and two variables, you should be able to substitute one equation into the other and solve for one variable (ideally the height of the mountain).