(a) You would need to use the Pythagorean Theorem, which is a2 + b2 = c2, where c is the hypotenuse of the right triangle. In this case, c is the height of the ramp. In order to solve this, let's have a = 0.345 m and b = 1.44 m. Then, we solve the equation as follows:
a2 + b2 = c2
(0.345)2 + (1.44)2 = c2
0.119025 + 2.0736 = c2
2.192625 = c2
√(2.192625) = √(c2)
1.48 m = c
Therefore, the height of the ramp would be 1.48 meters.
(b) When it's talking about the "angle the ramp makes with the horizontal", it's talking about the angle between the bottom of the ramp and the ground. To be able to solve that, you would need to draw a right triangle and use SOH CAH TOA.
If you don't know what SOH CAH TOA is, I'll explain real quick:
- SOH means "sin is opposite over hypotenuse", meaning that the length of the side opposite of the angle is divided by the hypotenuse.
- CAH means "cos is adjacent over hypotenuse", meaning that the length of the side adjacent of the angle is divided by the hypotenuse.
- TOA means "tan is opposite over adjacent", meaning that the length of the side opposite of the angle is divided by the adjacent side.
Going back to the problem, let's use CAH. For this problem we have a = 0.345 m as the vertical side and b = 1.44 m as the horizontal side. We'll call the angle x. Let's solve:
cos(x) = adj/hyp
cos(x) = 1.44/1.48
x = cos-1(1.44/1.48)
x = 13.35 degrees
At the length that the ramp is, it makes a 13.35-degree angle with the horizontal (ground).