Engineering Homework: Tower & Building Heights and Distances

In summary, a group of friends studying engineering are struggling with a math question that involves determining the height of a building and the distance between the building and a tower. They have attempted to use the Sine Rule and Cosine Rule, but feel that there is not enough information given in the problem. However, it is possible to solve the problem by setting up two equations using the unknown variables of distance and height and using algebra to solve for them.
  • #1
Xethron
2
0
Hey guys!

Me and all of my friends got this work for a mathematics question. But none of us can figure it out. We think they supplied too little information. We studying Engineering. I hope I posted it in the right place.

Homework Statement



The base of a building and the base of a tower are in the same horizontal plane. From the top of this building, the angle of elevation of the top of this tower is 10°. From a window 6m below the top of the building, the angle of depression of the base of the tower is 30°. The height of the tower is 120m.

Determine the height of the building.

Determine the distance between the building and the tower.

Homework Equations



Sine Rule and Cosine rule I figured... But there aint enough info to use ether.

The Attempt at a Solution



We basically drew it and filled in all the angles. One can find all the angles but with only one distance its pretty impossible to do anything else...

Thanks in advance!
 
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  • #2
You will have two unknown variables, x=distance between them and y=height of building. You also have two triangles that relate x and y in some way through angles. That will give you two equations.

Two equations can solve two unknowns exactly, so it is solvable. You will first need to find those 2 equations. Then it is just a matter of messy algebra to get x and y.
 

1. What is the purpose of calculating tower and building heights and distances in engineering homework?

The purpose of calculating tower and building heights and distances in engineering homework is to analyze and understand the structural integrity and stability of these structures. This information is crucial in ensuring safe and efficient construction, as well as identifying potential design flaws.

2. What are some common methods used to determine tower and building heights and distances?

Some common methods used to determine tower and building heights and distances include surveying, photogrammetry, laser scanning, and LiDAR. These methods involve using various instruments and techniques to measure and map out the dimensions of a structure.

3. What factors can affect the accuracy of calculating tower and building heights and distances?

The accuracy of calculating tower and building heights and distances can be affected by factors such as atmospheric conditions (e.g. wind, temperature), measurement errors, and the complexity of the structure's design. Additionally, the availability and precision of the measuring tools and techniques used can also impact the accuracy of the calculations.

4. How are tower and building heights and distances used in the construction process?

Tower and building heights and distances are used in the construction process to determine the placement and alignment of various structural elements, such as columns, beams, and foundations. This information is crucial in ensuring that the structure is built according to the design plans and meets safety standards.

5. Can tower and building heights and distances be calculated for existing structures?

Yes, tower and building heights and distances can be calculated for existing structures through various methods such as laser scanning and photogrammetry. These techniques involve capturing detailed measurements and images of the structure, which can then be used to calculate its height and other dimensions.

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