Random Adventures with Kevin using trigonometry to find the answers.
So Kevin is on top of a bus looking down on the angle of depression, which is 13, and the is 42 deg is the ground. What's the height of the bus? So its sin(42)=x/13 but x=13 xsin(42) and need to multiply 13 both sides, which give me x=8.7.
SOH CAH TOA
Kevin got bored from looking down the ground, so he went to his house and looked at the roof too if he could drive in the pool, but using trigonometry, he can tell if he can. So from him to the ceiling is x, and the angle is 79 deg, and the ground is 6. So he uses trig to figure out what's the line of slight. He finds out that 6/cos(79)=31.44ft. No can't jump because it's too dangerous.
Kevin is now at the park, and he ran from the slide to the ladder, which is 5 yards in front of a 10 ft ladder. He must now find the correct angle that he can go back to the ground. He uses tan-1(10/5)=63.4 degrees.
Kevin is now drawing his perfect triangle, but he imagines that a 90-foot wire is from the ground to the top of a 80-foot house, which is perpendicular to the level field. So Kevin is going to use sin-1(80/90) which give him 62.73 ft.