Angle elevation of sun is 25 degrees. Find the length the shadow cast by a tree 41 feet tall.
height of the tree O
________________________ = __
Tan 25= Cast shadow of the tree A
41
Cast shadow = ________
tAN 25
= 87.9
To find the length of the shadow cast by the tree, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the angle of elevation of the sun is 25 degrees. Let's assume the length of the shadow is x. The height of the tree is 41 feet.
Using the tangent function, we can set up the following equation:
tan(25 degrees) = height of the tree / length of the shadow
tan(25 degrees) = 41 / x
To find the length of the shadow, we need to isolate x. We can do this by rearranging the equation:
x = 41 / tan(25 degrees)
Now, we can use a calculator to calculate the value of tangent for 25 degrees:
tan(25 degrees) ≈ 0.4663
Substituting this value back into our equation:
x = 41 / 0.4663
x ≈ 87.93 feet
Therefore, the length of the shadow cast by the tree is approximately 87.93 feet.
To find the length of the shadow cast by a tree, you can use the concept of trigonometry and the tangent function.
The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the height of the tree, and the adjacent side is the length of the shadow.
Let's represent the height of the tree as h, the angle of elevation as θ, and the length of the shadow as s.
Given that the angle of elevation of the sun is 25 degrees and the height of the tree is 41 feet, we can set up the following equation:
tan(θ) = h / s
Plugging in the given values:
tan(25°) = 41 / s
Now, let's solve for the length of the shadow, s:
s * tan(25°) = 41
s = 41 / tan(25°)
To calculate this using a calculator, follow these steps:
1. Convert the angle from degrees to radians by multiplying it by π/180.
Angle in radians = 25° * π/180 ≈ 0.436332
2. Divide the height of the tree by the tangent of the converted angle to find the length of the shadow.
s = 41 / tan(0.436332) ≈ 91.669 feet
Therefore, the length of the shadow cast by the tree is approximately 91.669 feet.