A boy 1.4m tall stood 10m away from a tree of height 12m. calculate, correct to the nearest degree, the angle of elevation of the top of the tree from the boy's eyes
eyes are not on top of head ...
tan(θ) = (12 - 1.4) / 10
The height of the tree above the boy is 12-1.4=10.6
Using tan#= opposite /adjacent where # is the angle of elevation
tan#=10.6/10
hence #= 46.67 degrees
Answer
Well, let's see. If the boy is 1.4 meters tall and he is standing 10 meters away from the tree, we can use some simple trigonometry to find the angle of elevation.
First, we need to find the distance between the boy's eyes and the top of the tree. This can be calculated by adding the height of the tree (12m) to the boy's height (1.4m), giving us a total of 13.4m.
Next, we can use the tangent function to find the angle. 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 (12m) and the adjacent side is the distance between the boy and the tree (10m).
So, the angle of elevation can be calculated as the arctangent of (12/10). Plugging that into a calculator, we get approximately 50.19 degrees.
Therefore, the angle of elevation of the top of the tree from the boy's eyes is around 50 degrees (approximated to the nearest degree).
Hope this helps, and I hope my calculations weren't too much of a tree-mendous feat for you!
To calculate the angle of elevation of the top of the tree from the boy's eyes, we can use trigonometry. In this case, we can use the tangent function.
Let's define the height of the tree as 'a' and the distance between the boy and the tree as 'b'. In this scenario, 'a' is given as 12m and 'b' is given as 10m.
The tangent of an angle is equal to the opposite side divided by the adjacent side in a right-angled triangle. In this case, the angle is the angle of elevation, the opposite side is the height of the tree (a), and the adjacent side is the distance from the boy to the tree (b).
Therefore, we can start by calculating the value of the tangent function:
tan(angle) = opposite / adjacent
tan(angle) = a / b
tan(angle) = 12 / 10
Next, to find the angle, we need to take the inverse tangent (also known as arctangent) of both sides of the equation. This will give us the angle from the tangent value:
angle = atan(tan(angle))
angle = atan(12 / 10)
Using a scientific calculator or an online calculator, we can find the value of atan(12/10) to be approximately 1.157.
Now, to convert the angle from radians to degrees, we multiply by 180/π (approximately 57.3 degrees):
angle_degrees = angle_radians * (180/π)
angle_degrees = 1.157 * (180/π)
angle_degrees ≈ 66.48 degrees
Therefore, the angle of elevation of the top of the tree from the boy's eyes is approximately 66.48 degrees.