A boy is 1.5m tall is away from a hut 24m high what is the angle of elevation of the top of the hut explain with diagram
how far away is the boy from the hut?
Draw your diagram, and you will see it makes a difference.
To find the angle of elevation of the top of the hut, we can use trigonometry. Let's draw a diagram to help visualize the situation.
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/
/|
/ |
boy / | hut
/ |
/θ |
/_____|
```
In the diagram, the boy is standing at a certain distance from the hut, and we want to find the angle of elevation θ, which is the angle between the ground (horizontal line) and the line of sight from the boy to the top of the hut.
Using trigonometry, we know that 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 hut (24m) and the adjacent side is the distance between the boy and the hut.
Let's call this distance "d". To find d, we can use the Pythagorean theorem since we have a right-angled triangle:
d² + 1.5² = h²
Simplifying this equation, we get:
d² + 2.25 = 576
d² = 576 - 2.25
d² = 573.75
Taking the square root of both sides, we find:
d ≈ 23.93m
Now that we have the value of d, we can use tangent to find the angle θ:
tan(θ) = opposite/adjacent
tan(θ) = 24/23.93
θ = tan^(-1)(24/23.93)
Using a calculator, we find that:
θ ≈ 44.9°
Therefore, the angle of elevation of the top of the hut from the boy's position is approximately 44.9°.
To find the angle of elevation of the top of the hut, we need to draw a diagram and use the concept of trigonometry.
Here's how you can calculate it:
Step 1: Draw a diagram representing the situation. Draw a horizontal line to represent the ground, and a vertical line to represent the hut. Mark a point on the ground to represent the position of the boy, and label it as "B." Label the top of the hut as "H." Draw a line connecting point B to point H to represent the line of sight.
B
/
/
/
/
/
/ 24m (height of the hut)
/
/
/
/
H
Step 2: Mark the height of the boy on the line segment BH. Label it as "1.5m."
B
/|
/ |
/ |
/ | 1.5m (height of the boy)
/ |
/ |
/ |
/ |
/ |
/ |
H
Step 3: Now, we can use the concept of trigonometry to find the angle of elevation. In this case, the tangent of the angle of elevation is equal to the opposite side (1.5m) divided by the adjacent side (24m). The angle of elevation, theta, can be found using the inverse tangent function (tan⁻¹).
tan(theta) = opposite/adjacent
tan(theta) = 1.5m/24m
theta = tan⁻¹(1.5m/24m)
Step 4: Use a calculator to find the value of theta by entering the above equation. The resulting value will be the angle of elevation in degrees.
theta ≈ 3.82 degrees
Therefore, the angle of elevation of the top of the hut is approximately 3.82 degrees.
Note: The angle of elevation refers to the angle at which the line of sight (BH) is inclined upwards from the horizontal line (ground).