To the nearest foot, how far up the building does the ladder reach in Figure 1?

Question

A 12 foot ladder is placed against the side of a building, forming a right triangle as shown in Figure 1 below. The bottom of the ladder is 7 feet from the base of the building. In order to ingrease the height to which the ladder reaches, the ladder is moved closer to the base of the building, increasing the angle the ladder makes by the ground by 20º as shown in figure 2.

Answer 1

It used to reach 9.75 feet at an angle of 54.3 degrees

Now it reaches 11.55 feet at an angle of 74.3 degrees

12^2 -49^2 = 9.75^2

12^2 -3.244^2 = 11.55^2

the ladder is the hypotenuse of a right triangle with base originally 7 and then 3.244, height originally 9.75 and then 11.55