A bag 1.4m tall stood 10m away from a tree of height 12m. Calculate the nearest degree the angle of elevation of tree from the boys eyes.mark a diagram
tanθ = (12-1.4)/10
Tan o =(,12-1.4)\10
To calculate the angle of elevation of the tree from the boy's eyes, we can use trigonometry. Let's assume that the boy's eyes are at a height of h meters from the ground.
First, let's draw a diagram to visualize the situation:
/|
/ |
Tree / | h = ?
/ | \
/ | \
Boy |______ \ Bag
Distance = 10m
From the diagram, we can see that we have a right-angled triangle formed by the boy, the tree, and the line connecting them.
Using the tangent function, we can calculate the angle of elevation:
tan(angle) = Opposite / Adjacent
tan(angle) = height of the tree / distance from the tree
tan(angle) = 12m / 10m
tan(angle) = 1.2
To find the angle, we take the arctan of both sides:
angle = arctan(1.2)
Using a calculator, we find that:
angle ≈ 50.19 degrees
Therefore, the nearest degree of the angle of elevation of the tree from the boy's eyes is approximately 50 degrees.
To solve this problem, we can use the concept of trigonometry. Let's draw a diagram to visualize the scenario:
```
A (Boy's eyes)
|\
| \
| \ 12m (Height of tree)
| \
| \
| \
| \
| \
B-------C (Top of the bag)
10m
```
In this diagram, A represents the boy's eyes, B represents the top of the bag (1.4m tall), and C represents the top of the tree (12m tall). We are given that AB is 10m, BC is 1.4m, and AC is 12m.
To calculate the angle of elevation of the tree from the boy's eyes, we need to find the angle θ at point B. We can use the tangent function to find this angle:
tan(θ) = opposite/adjacent
In this case, the opposite side is AC (12m) and the adjacent side is AB (10m), so we have:
tan(θ) = 12/10
To find the angle θ, we can use the inverse tangent function (arctan) on both sides:
θ = arctan(12/10)
Using a calculator, the value of arctan(12/10) is approximately 51.34 degrees.
Therefore, the nearest degree angle of elevation of the tree from the boy's eyes is 51 degrees.