Question

1. Suppose that you are watching the tree warden trim branches from a large tree in your yard. He has climbed up 15 meters and his assistant is holding a rope that will be used to guide the branch when it falls. To the nearest meter, how long is the rope?

2. For XYZ, what is the measure of the smallest angle to the nearest tenth of a degree? (ZY = 8) (YX = 3.5) (ZX = x )

Answer 1

In item# 1, we are only given with the height of the tree a=15 meters and we are asked to solve for the hypotenuse. Since we are not given with angle created between the rope the ground level we will assign it as ∠A = ∅
Solving for the length of the rope, we have
sin A = 15/Length of rope
Length of rope = 15 meters / sin A

In item#2, assuming that it is a right triangle we have:
8 ²= x²+3.5²
x=7.2

The smallest angle:
sin Z =3.5/8
Z = 25.95°