Answer:
Step-by-step explanation:
I am assuming that the functions are:
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Answer:
54.8 feet
Step-by-step explanation:
We assume that the distance of interest is the direct line distance from the observation point to the bottom of the monument, segment PH in the diagram below.
This can be found using the Law of Sines.
∠PMH is the complement of the angle of elevation to the top of the monument, so is 40°.
∠MPH is the difference in the angles of elevation, so is 28°.
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The Law of Sines tells us the ratio of side lengths is the same as the ratio of the sines of the opposite angles, so ...
PH/MH = sin(∠PMH)/sin(∠MPH) = sin(40°)/sin(28°)
Multiplying by MH, we can find the length of PH:
PH = (40 ft)(sin(40°)/sin(28°)) ≈ 54.7669 ft
PH ≈ 54.8 ft . . . . the distance Pete must climb to reach the monument.
Check out the attached image.
Point P = base of the pole
Point Q = point where the pole broke
Point R = point where the tip of the pole landed on the ground.
We're told that "28 feet are still sticking straight out of the ground", so PQ = 28 is the vertical leg of the right triangle. The horizontal leg is unknown, so we'll call it x, making PR = x. The hypotenuse is QR = 53 because 81-28 = 53. This is the left-over amount after taking off the 28 feet initially out of the ground from the 81 ft pole.
In short, we have these three values
a = x is one of the legs
b = 28 is the other leg
c = 53 is the hypotenuse
Use the Pythagorean Theorem to find x
a^2 + b^2 = c^2
x^2 + 28^2 = 53^2
x^2 + 784 = 2809
x^2 = 2809 - 784
x^2 = 2025
x = sqrt(2025)
x = 45
The end of the pole is 45 feet away from the base
Answer: 45 feet
Point P = base of the pole
Point Q = point where the pole broke
Point R = point where the tip of the pole landed on the ground.
We're told that "28 feet are still sticking straight out of the ground", so PQ = 28 is the vertical leg of the right triangle. The horizontal leg is unknown, so we'll call it x, making PR = x. The hypotenuse is QR = 53 because 81-28 = 53. This is the left-over amount after taking off the 28 feet initially out of the ground from the 81 ft pole.
In short, we have these three values
a = x is one of the legs
b = 28 is the other leg
c = 53 is the hypotenuse
Use the Pythagorean Theorem to find x
a^2 + b^2 = c^2
x^2 + 28^2 = 53^2
x^2 + 784 = 2809
x^2 = 2809 - 784
x^2 = 2025
x = sqrt(2025)
x = 45
The end of the pole is 45 feet away from the base
Answer: 45 feet