Question

Om looks up to the top of the water tower at an angle of elevation of 44. He walked 87 meters in a straight yards the tower. Then she looks to the top of the tower at an angle of elevation of 51. How far is Om from the the tower.

Answer 1

Explanation:

To find the distance between Om and the water tower, we can use trigonometry and the concept of similar triangles.

First, let's consider the angle of elevation of 44 degrees. We can set up a right triangle with the height of the water tower as the vertical side and the distance between Om and the tower as the horizontal side. The angle of elevation is the angle between the horizontal side and the hypotenuse.

Using trigonometry, we can use the tangent function to find the height of the tower:

tan(44) = height / distance

Now, let's consider the angle of elevation of 51 degrees. We can set up another right triangle, similar to the first one, but with a different angle and distance.

Using trigonometry again, we can use the tangent function to find the height of the tower in this case:

tan(51) = height / (distance + 87)

We have two equations with two unknowns (height and distance), so we can solve them simultaneously to find the values.

Let's solve for the height in both equations:

height = distance * tan(44)

height = (distance + 87) * tan(51)

Since both equations equal the height, we can set them equal to each other:

distance * tan(44) = (distance + 87) * tan(51)

Now, we can solve this equation for the distance.

Answer 2

Om is approximately 29.12 meters away from the water tower.

Explanation:

* (top of water tower)

/| 51°

/ |

/ |

87m / |

/ |

/ |

/ |

-----*------- |

44°

```

From the diagram, we can see that there are two right triangles: Om to the base of the water tower, and Om to the top of the water tower. We can use trigonometry to solve for x, which represents the distance between Om and the tower.

First, let's find the height of the water tower using the first angle of elevation:

Opposite = tower height

Adjancent = distance from Om to base of tower

Tan(44) = Opposite/Adjacent

Tan(44) = x/87

Opposite = Tan(44) * 87

Opposite = 96.09 meters

Now, we can find x using the second angle of elevation:

Opposite = tower height (same as calculated earlier)

Adjacent = distance from Om to top of tower + 87

Tan(51) = Opposite/Adjacent

Tan(51) = 96.09/x + 87

x + 87 = 96.09/Tan(51)

x = 96.09/Tan(51) - 87

x = 29.12 meters