Ramon secured an 8 foot volleyball net pole to the ground with a rope attached to the top of the pole and staked in the ground, 5 feet from the base of the vertical pole. What is the angle formed between the top of the pole and the rope? Round your answer to the nearet degree(1 point)
Write the equation to represent the problem.
___^−1 x = __
Question 2
Use the equation you indicated above to solve for x.(1 point)
x = __°
To find the angle formed between the top of the pole and the rope, we can use trigonometry. The angle formed between the top of the pole and the rope is equal to the inverse tangent of the adjacent side (5 ft) divided by the opposite side (8 ft).
So, the equation to represent the problem is:
tan^(-1)x = 5/8
Now, we can solve for x:
x = tan^(-1)(5/8) ≈ 32°
Therefore, the angle formed between the top of the pole and the rope is approximately 32°.
A business is building a handicap-accessible ramp at the entrance of the building. They want the slope to be a 1:15 ratio. In 1 - 2 sentences, explain how to find the angle of elevation of the ramp. What is the angle of elevation to the nearest hundereth of a degree? Show all your work.
To find the angle of elevation of the ramp, we can use the inverse tangent function. The tangent of the angle of elevation is equal to the rise (the vertical height of the ramp) divided by the run (the horizontal length of the ramp). With a 1:15 ratio, the tangent of the angle is 1/15.
First, we need to calculate the slope length using Pythagorean theorem:
slope length = √(1^2 + 15^2)
slope length = √(1 + 225)
slope length = √226
slope length ≈ 15.03 ft
Now, we find the angle of elevation:
tan^(-1) (1/15) = tan^(-1) (1/15)
tan^(-1) (1/15) ≈ 3.814°
Therefore, the angle of elevation of the ramp is approximately 3.81°.
Cherry is flying a kit that is 27 meters above the ground. The angle formed with the string and the ground is 39°. How long is the string? Write the equation and solve showing all of your work to support your answer. Round your answer to the nearest tenth.
To find the length of the string, we can use trigonometry. The length of the string is the hypotenuse of the right triangle formed by the kite string, the ground, and the height of the kite.
We can use the sine function to calculate the length of the string:
sin(39°) = opposite/hypotenuse
sin(39°) = 27/hypotenuse
Now, we need to solve for the hypotenuse (length of the string):
hypotenuse = 27/sin(39°)
hypotenuse ≈ 43.4 meters
Therefore, the length of the string is approximately 43.4 meters.
A 25-rope is tied to the top of an 8-foot vertical pole and the rope is pulled tight and attached to the ground. What is the angle formed between the rope and the pole? Write the equation and solve showing all of your work to support your answer. Round your answer to the nearest tenth
To find the angle formed between the rope and the pole, we can use trigonometry. The angle we're looking for is the angle between the rope and the pole, which is the same as the angle between the rope and the ground (since the pole is vertical).
The length of the rope is the hypotenuse of the right triangle formed by the rope, the pole, and the ground. We can use the cosine function to calculate the angle:
cos(angle) = adjacent/hypotenuse
cos(angle) = 8/25
angle = arccos(8/25)
Now we can solve for the angle:
angle ≈ arccos(8/25) ≈ 70.5 degrees
Therefore, the angle formed between the rope and the pole is approximately 70.5 degrees.