The angle of elevation of the sun is 78 degrees. How long is the shadow of a 30m tree?
To find the length of the shadow of a tree, we can use the concept of trigonometry.
Let's assume that the length of the shadow is represented by "x".
In this case, we have the angle of elevation (from the ground to the top of the tree) as 78 degrees.
We can use the tangent function to relate the angle of elevation and the length of the shadow:
tan(angle) = opposite / adjacent
In this case, the opposite side is the height of the tree, which is 30m, and the adjacent side is the length of the shadow, which is "x".
So, we can write the equation as:
tan(78) = 30 / x
To find the value of x, we isolate it on one side of the equation. We can rearrange the equation to solve for x:
x = 30 / tan(78)
Using a calculator, we can evaluate the equation:
x ≈ 8.57 meters
Therefore, the length of the shadow of the 30-meter tree is approximately 8.57 meters.
To find the length of the shadow of the tree, we can use trigonometry and the angle of elevation of the sun.
Let's consider the tree as a vertical line, the shadow as a horizontal line, and the angle of elevation of the sun as the angle between the tree and its shadow.
We can use the tangent function to find the length of the shadow. The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
In this case, the opposite side is the length of the tree (30m), and the adjacent side is the length of the shadow (unknown). The tangent of the angle of elevation (78 degrees) would be equal to the length of the tree divided by the length of the shadow.
So, we have the equation:
tan(78 degrees) = opposite/adjacent
Plugging in the known values, we get:
tan(78 degrees) = 30m/adjacent
Now, we can isolate the length of the shadow:
adjacent = 30m / tan(78 degrees)
Using a calculator, we can determine the value of tan(78 degrees) as approximately 4.2866.
Substituting this value into the equation:
adjacent = 30m / 4.2866
Calculating the result:
adjacent ≈ 6.998m
Therefore, the length of the shadow of the 30m tree would be approximately 6.998 meters.