Anonymous
2 hours ago
A boy is 1.5m tall standing 12m away from a church building which has a tower on top of its roof.the top of the cross of the tower is 14.6m away from the boys head (eyes) . An angle of 31^0 calculate?
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ChatGPT
2 hours ago
To solve this problem, we can use trigonometry. Let's denote the height of the tower as h.
From the information given, we can set up a right triangle with the boy's height, the distance from the boy to the building, and the height of the tower. The angle between the boy's line of sight and the ground is 31 degrees.
Using the tangent function, we can set up the following equation:
tan(31 degrees) = h / 12m
Solving for h, we get:
h = 12m * tan(31 degrees)
h = 7.1m
Therefore, the height of the tower is 7.1m.
From the information given, we can set up a right triangle with the boy's height, the distance from the boy to the building, and the height of the tower. The angle between the boy's line of sight and the ground is 31 degrees.
Using the tangent function, we can set up the following equation:
tan(31 degrees) = h / 12m
Solving for h, we get:
h = 12m * tan(31 degrees)
h = 7.1m
Therefore, the height of the tower is 7.1m.
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Google Gemini AI
2 hours ago
Step 1: Draw a diagram
[Image of a diagram with a boy, a church building, and a tower]
Step 2: Identify the known and unknown values
- Known:
- Boy's height: 1.5m
- Distance from boy to building: 12m
- Distance from boy's head to top of cross: 14.6m
- Angle of elevation: 31°
- Unknown:
- Height of tower
Step 3: Use trigonometry to find the height of the tower
Case 1: Angle of depression
From the diagram, we can see that the angle of depression from the boy's eyes to the bottom of the tower is:
```
90° - 31° = 59°
```
Using trigonometry, we have:
```
tan 59° = (height of tower) / 12
```
Solving for the height of the tower:
```
height of tower = 12 - tan 59° ≈ 24.5m
```
Case 2: Angle of elevation
Note that the question mentions the angle of elevation from the boy's eyes to the top of the cross. This means we need to use the height of the tower minus the height of the boy, which is:
```
height of tower - height of boy = 24.5m - 1.5m = 23m
```
Step 4: Calculate the distance from the boy's head to the bottom of the tower
Using trigonometry, we have:
```
tan 31° = (distance from boy's head to bottom of tower) / 12
```
Solving for the distance:
```
distance from boy's head to bottom of tower = 12 - tan 31° ≈ 7.8m
```
Therefore, the height of the tower is 23m and the distance from the boy's head to the bottom of the tower is 7.8m.
[Image of a diagram with a boy, a church building, and a tower]
Step 2: Identify the known and unknown values
- Known:
- Boy's height: 1.5m
- Distance from boy to building: 12m
- Distance from boy's head to top of cross: 14.6m
- Angle of elevation: 31°
- Unknown:
- Height of tower
Step 3: Use trigonometry to find the height of the tower
Case 1: Angle of depression
From the diagram, we can see that the angle of depression from the boy's eyes to the bottom of the tower is:
```
90° - 31° = 59°
```
Using trigonometry, we have:
```
tan 59° = (height of tower) / 12
```
Solving for the height of the tower:
```
height of tower = 12 - tan 59° ≈ 24.5m
```
Case 2: Angle of elevation
Note that the question mentions the angle of elevation from the boy's eyes to the top of the cross. This means we need to use the height of the tower minus the height of the boy, which is:
```
height of tower - height of boy = 24.5m - 1.5m = 23m
```
Step 4: Calculate the distance from the boy's head to the bottom of the tower
Using trigonometry, we have:
```
tan 31° = (distance from boy's head to bottom of tower) / 12
```
Solving for the distance:
```
distance from boy's head to bottom of tower = 12 - tan 31° ≈ 7.8m
```
Therefore, the height of the tower is 23m and the distance from the boy's head to the bottom of the tower is 7.8m.
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