The angle of elevation of the sun is 22 degrees. How long is the shadow of a 15m tree, to the nearest metre?
done when you posted as nj
20 meter
To find the length of the shadow of a tree, you can use trigonometry. In this case, you need to use the tangent function because you have the angle of elevation and the opposite side length (height of the tree), and you want to find the adjacent side length (length of the shadow).
The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the tree (15m) and the angle of elevation is 22 degrees.
So, let's calculate the length of the shadow:
1. Start by taking the tangent of the angle of elevation:
tan(22°) = opposite/adjacent
2. Substitute the known values:
tan(22°) = 15m/adjacent
3. Rearrange the equation to solve for the adjacent side:
adjacent = 15m / tan(22°)
4. Calculate the value using a calculator:
adjacent ≈ 15m / 0.4040
adjacent ≈ 37.13m
Therefore, the length of the shadow of the 15m tree is approximately 37.13 meters when rounded to the nearest meter.