Finding the Height of a Building

[pointintime]

Homework Statement

56. Finding the Height of a Building
To measure the height of a building, two sightings are taken a distance of 50 feet apart. if the first angle of elevation is 40 degrees and the seconds is 32 degrees, what is the height of the building?

Homework Equations

defintion of tan theta

The Attempt at a Solution

http://img40.imageshack.us/img40/148/asdasdye.jpg

(def of tan theta = a^-1 o)a = o
opposite = adjacent tan theta

written with respect to the first angle

opposite = (adjacent 1 + adjacent 2) tan theta one

were adjacent 1 is the 50 feet

written for the second angle

opposite = adjacent 2 tan theta two

set them equal to each other

(adjacent 1 + adjacent 2) tan theta one = adjacent 2 tan theta two

distripute

adjacent 1 tan theta one + adjacent 2 tan theta one = adjacent 2 tan theta two

subtract from both sides

adjacent 1 tan theta one = adjacent 2 tan theta two - adjacent 2 tan theta one

factor or whatever

adjacent 1 tan theta one = adjacent 2 (tan theta two - tan theta one)

muliply by inverse to solve for adjacent 2

(adjacent 1 tan theta one = adjacent 2 (tan theta two - tan theta one)) ((tan theta two - tan theta one)^-1

adjacent two = (tan theta two - tan theta one)^-1 adjacent 1 tan theta one

plug and chug for adjacent two

adjacent two = (tan 32 degrees - tan 40 degrees)^-1 (50 ft) tan theta 40 degrees

I got negative 195.8 feet?

 

[nate808]

Thank you for your post. I would like to provide some feedback on your solution.

Firstly, your use of the definition of tangent (tan) is correct. However, in your attempt at a solution, you have made some mathematical errors.

In the step where you distribute, you have made a mistake in the second term. It should be "adjacent 1 tan theta two" instead of "adjacent 2 tan theta two". This mistake carries on to the next step where you subtract from both sides. It should be "adjacent 1 tan theta two" instead of "adjacent 2 tan theta two - adjacent 2 tan theta one".

Also, in the step where you factor, it should be "adjacent 1 (tan theta one - tan theta two)" instead of "adjacent 2 (tan theta two - tan theta one)".

Finally, when you multiply by the inverse, you have made a mistake in the first term. It should be "(adjacent 1 tan theta one)^-1" instead of "adjacent 1 tan theta one".

After correcting these mistakes, the final equation should be:

adjacent 2 = (tan theta two - tan theta one)^-1 * adjacent 1 * tan theta one

Plugging in the values, we get:

adjacent 2 = (tan 32 degrees - tan 40 degrees)^-1 * 50 ft * tan 40 degrees

Solving this equation will give us the correct value for adjacent 2, which can then be used to calculate the height of the building.

I hope this helps in your understanding of the problem. Remember to always double check your calculations and equations to avoid errors. Keep up the good work in your scientific endeavors!

 

[Architeuthis Dux]

I would like to point out that the solution provided is incorrect. The height of the building cannot be a negative value. It is important to double check the calculations and make sure the units are consistent throughout the problem. Additionally, it would be helpful to label the sides of the triangle and clearly define the variables used in the solution. A more accurate approach would be to use the trigonometric identity tan (a-b) = (tan a - tan b) / (1 + tan a * tan b) and solve for the height using the given angles and distance. It is also important to note that in order to accurately measure the height of a building using this method, the distance between the two sightings should be greater than the height of the building.