Tyler buys potting soil every January to plant his vegetable garden. This year he bought 15 25-pound bags of potting soil. He must push them up a 5-foot high ramp to his truck. The horizontal distance from the base of the ramp to the truck is 12 feet. Find the length of the ramp.(1 point)
The ramp is ___ feet long.
Using the Pythagorean theorem, we can calculate the length of the ramp.
Let x be the length of the ramp.
According to the Pythagorean theorem,
(x^2) = (5^2) + (12^2)
x^2 = 25 + 144
x^2 = 169
x = 13
Therefore, the length of the ramp is 13 feet.
Use the Pytahgorean triple (11, 60, 61) to find a new Pythagorean triple that contains 183.(3 points)
Write the Pythagorean triple in order from smallest to largest ( __, __, __)
To find a new Pythagorean triple that contains 183, we can use the Pythagorean triple (11, 60, 61) and multiply each number by 3 to get a product of 183, since 61 * 3 = 183.
(33, 180, 183)
Therefore, the new Pythagorean triple containing 183 is (33, 180, 183).
Charles is flying a helicopter at 1,350 feet and sees an airplane 2,400 feet in front of but also above him. Charles knows the angle of elevation is 54°. How far is the airplane from the ground?(1 point)
Responses
3303 feet
3303 feet
2761 feet
2761 feet
4653 feet
4653 feet
3094 feet
We can use trigonometry to solve this problem.
Let x be the distance from the airplane to the ground.
Using the tangent function, tan(54°) = x / 2400
x = 2400 * tan(54°)
x ≈ 2375.1 feet
Therefore, the airplane is approximately 2375.1 feet from the ground.
None of the provided answer options matches this result.
If ∠A=52°
and b = 22
mi., then how long is side c
to the nearest tenth of a mile? Picture is not drawn to scale.
(1 point)
Responses
28.2 mi.
28.2 mi.
17.2 mi.
17.2 mi.
27.9 mi.
27.9 mi.
35.7 mi.
35.7 mi.
To find the length of side c, we can use the Law of Sines, which states that a/sin(A) = b/sin(B) = c/sin(C).
We know that angle A = 52°, side b = 22 miles.
Since we are finding side c opposite angle C, we will find angle B first.
Angle B = 180° - 52° - 90° = 38°
Now, we can use the Law of Sines:
c / sin(C) = b / sin(B)
c / sin(90°) = 22 / sin(38°)
c = 22 / sin(38°)
c ≈ 35.7 miles
Therefore, the length of side c to the nearest tenth of a mile is approximately 35.7 miles.
The correct response from the options provided is: 35.7 mi.
For a ramp with an angle of elevation of 14° and a height of 2.5 feet. How long is the ramp? Round your answer to the nearest tenth.
(1 point)
Write the equation to represent the problem.
__14° = ___
Question 2
Use the equation indicated above to solve for the desired side. Round answer to the nearest tenth. (1 point)
The ramp is __ feet long
For a ramp with an angle of elevation of 14° and a height of 2.5 feet, we can use trigonometry to solve for the length of the ramp.
1. Write the equation to represent the problem:
In a right triangle, the tangent of an angle equals the opposite side over the adjacent side.
tan(14°) = 2.5 / x, where x is the length of the ramp.
2. Use the equation to solve for the length of the ramp:
tan(14°) = 2.5 / x
x = 2.5 / tan(14°)
x ≈ 9.6 feet
Therefore, the ramp is approximately 9.6 feet long.
The equation is:
tan(14°) = 2.5 / x
The ramp is 9.6 feet long.
A cat climbs onto a roof and looks down at you. You are standing 12 feet away from the house and there is a 18-foot diagonal between you and the cat. What is the angle of depression from the cat to you? Round your answer to the nearest whole number.(1 point)
___ ^−1 x = ___
Question 2
Use the above equation to solve for x.(1 point)
x= __°