Angle of elevation

Question

From a point level with the base of a water tower the angle of elevation to the bottom of the water tank is 38° to the top of the water tank is 47° if the water tank itself is 20 feet high what is the height of the tower and tank together. Can you please give the exact steps and why you sued that if possible

Answer 1

There are 2 equations here.

Let x = the horizontal distance from the base of the water tower

Let y = the vertical distance from the ground to the bottom of the water tank

tan 38 = y/x

tan 47 = (y+20)/x

This can be solved by substitution, solving each equation for x

x=y/tan 38

x=(y+20)/tan 47

Set the 2 equations equal to one another. Now you have one equation one unknowns.

y/tan 38 = (y+20)/tan 47

Cross multiply to get rid of the fractions. Can you solve from there?