Yusuf is 12m away from the building and he observes that the angle of elevation of the building in 52,he is 1.5m tall find the height of the building use a scale of 1cm to represent 3m
Let's draw a diagram to visualize the problem.
We have a right-angled triangle formed by Yusuf, the building, and the ground.
Yusuf is standing at a point 12m away from the base of the building. The angle of elevation from Yusuf to the top of the building is 52 degrees. We need to find the height of the building.
Let's assume that the height of the building is 'x'. Since Yusuf's height is 1.5m, the total height from the ground to the top of the building will be x + 1.5m.
Now, let's use the tangent function:
tan(angle) = opposite/adjacent
We have the opposite side (x + 1.5m) and the adjacent side (12m).
tan(52) = (x + 1.5) / 12
To find the value of x, rearrange the equation:
(x + 1.5) = 12 * tan(52)
x = (12 * tan(52)) - 1.5
Using a scale of 1cm to represent 3m, we'll need to convert the height of the building to centimeters.
The height in centimeters = x * (1cm/3m)
Now, substitute the value of x into the equation:
Height in centimeters = [(12 * tan(52)) - 1.5] * (1cm/3m)
Calculating this expression will give you the height of the building in centimeters.
To find the height of the building, we can use trigonometry.
Step 1: First, let's draw a diagram to better understand the problem.
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| / |
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| / |
|/ |
Yusuf (1.5m) Building
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Step 2: We have a right triangle formed by Yusuf, the building, and the line of sight.
```
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| /|
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| / θ | Opposite
| / | (Height of the building)
|/ |
Yusuf (1.5m) Building
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Adjacent
(12m)
```
Step 3: We can use the tangent function to find the height of the building.
```
tan(θ) = Opposite/Adjacent
```
In this case, the angle of elevation is given as 52 degrees, the opposite side is the height of the building, and the adjacent side is 12m.
```
tan(52°) = Opposite/12m
```
Step 4: Calculate the ratio of the opposite side to the adjacent side using the tangent function.
```
Opposite side = tan(52°) * 12m
```
Step 5: Convert the height to centimeters according to the given scale of 1cm represents 3m.
```
Height of the building (in cm) = (tan(52°) * 12m) * 3
```
Let's calculate the height of the building using these steps:
```
Height of the building = (tan(52°) * 12) * 3
Height of the building ≈ 19.45m
```
Therefore, the height of the building, according to the given scale of 1cm to represent 3m, is approximately 19.45m.