Answer:
1. 33 foot
2. 6.2 foot
Explanation:
1.
Let's denote the height of the tree by "h". We can use the tangent function to solve the problem:
tangent of the angle of elevation = opposite / adjacent
In this case, the opposite side is the height of the tree, and the adjacent side is the distance from the tree to the point on the ground where the angle of elevation is measured. So we have:
tan(35) = h / 47
To solve for "h", we can multiply both sides by 47:
h = 47 tan(35)
Using a calculator, we get:
h ≈ 32.9 feet
So the height of the tree to the nearest foot is 33 feet.
2.
Let's call the distance we're trying to find "x". We can use trigonometry to relate the angle and the length of the guy wire to the distance "x". Specifically, we can use the sine function:
sine of the angle = opposite / hypotenuse
In this case, the opposite side is the distance "x", and the hypotenuse is the length of the guy wire, which is 8 feet. So we have:
sin(51) = x / 8
To solve for "x", we can multiply both sides by 8:
x = 8 sin(51)
Using a calculator, we get:
x ≈ 6.2 feet
So the stake is about 6.2 feet from the foot of the stop sign, to the nearest tenth of a foot.