The angle of elevation of the sun is 22 degrees. How long is the shadow of a 15m tree, to the nearest metre?
after making your sketch you should see that
tan22° = 15/x
x = 15/tan22 = appr37.1 m
To find the length of the shadow of the tree, we can use the properties of trigonometry. In this case, we can use the concept of tangent.
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this scenario, the opposite side is the height of the tree (15m), and the adjacent side is the length of the shadow.
Let's use the formula for tangent:
tangent(angle) = opposite/adjacent
In this case, we know that the angle of elevation of the sun is 22 degrees and the height of the tree is 15m. We need to find the length of the shadow (adjacent side).
So, we can rearrange the formula to solve for the adjacent side:
adjacent = opposite / tangent(angle)
adjacent = 15m / tangent(22 degrees)
Now, we can use a calculator to find the tangent of 22 degrees:
tangent(22 degrees) ≈ 0.4040
Plugging this value back into the formula, we get:
adjacent ≈ 15m / 0.4040
adjacent ≈ 37.13m
Therefore, the length of the shadow of the 15m tree, to the nearest meter, is approximately 37 meters.