If the distance from the top of a building to the tip of its shadow is 150 feet and the sun makes a 75 degree angle with the wall as shown in the image below, what is the length of the shadow?
guessing what your diagram would look like,
sin 75 = x/150
x = 150sin75 = appr 144.9 ft
To find the length of the shadow, we can use trigonometry. We know that the angle between the sun and the wall is 75 degrees and the height of the building is 150 feet.
Let's assume the length of the shadow is "x" feet.
We can use the tangent function to find the length of the shadow:
tan(angle) = opposite/adjacent
In this case, the opposite side is the height of the building (150 feet), and the adjacent side is the length of the shadow (x feet).
So, we have:
tan(75°) = 150/x
To solve for x, we can rearrange the equation:
x = 150 / tan(75°)
Now, we can calculate the length of the shadow:
x ≈ 150 / tan(75°) ≈ 150 / 3.732 ≈ 40.21 feet
Therefore, the length of the shadow is approximately 40.21 feet.
To find the length of the shadow, we can use trigonometry. Specifically, we can use the tangent function since we have the opposite and adjacent sides of the right triangle formed.
Let's denote the length of the shadow as 'x', the height of the building as 'h', and the angle formed by the sun and the wall as 'θ'. We have the following information:
- The distance from the top of the building to the tip of its shadow is 150 feet, which represents the hypotenuse of the right triangle.
- The height of the building is the side opposite to the angle θ.
- The length of the shadow is the side adjacent to the angle θ.
Now, applying the tangent function:
tan(θ) = opposite / adjacent
tan(θ) = h / x
We need to find 'x', so we rearrange the equation to isolate 'x':
x = h / tan(θ)
Substituting the given values:
x = 150 / tan(75°)
To find the answer, we can now calculate the value of 'x' using a calculator or math software that can handle trigonometric functions.