SOLUTION: I have a problem here that states. There are two buildings (I will call them "nearby building" and "skyscraper") and need to find the height of both buildings. -What we are told

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Question 1003675: I have a problem here that states. There are two buildings (I will call them "nearby building" and "skyscraper") and need to find the height of both buildings.
-What we are told is the distance between them is 75m.
-The angle of elevation from the base of the "nearby building" to the top of the "skyscraper" is 54 degrees.
-The angle of elevation from the roof of the "nearby building" to the top of the "skyscraper" is 45 degrees.
Here is the solution I have came up with, knowing the angle from the "nearby building" to the top of the "skyscraper" and considering the other angle is 36. I need to then find the tan(36).
tan36=75/x
x= 75/tan36
x= 103.2
So the skyscraper would be 103.2 meters tall
For the "nearby building" we would do the same
tan45=75/x
x=75/tan45
x=75
Then find the difference 103.2-75=28.2
The nearby building would then be 28.2 meters tall
I wish I could include the graphic I drew to explain it visually, sorry if I didn't word this well enough to understand. We are also told to round to the nearest tenth.
Found 3 solutions by josgarithmetic, mananth, MathTherapy:
Answer by josgarithmetic(39621)   (Show Source): You can put this solution on YOUR website!
I have analyzed to be able to see part of the description. I will explain the drawing I made instead of show it.

Horizontal segment 75 meters or units. At the left is perpendicular segment of height n; At the right is perpendicular segment of height y. n corresponds to the nearby building, and y corresponds to the skyscraper. The angle described 54 degrees is at the bottom of the nearby building with hypotenuse running to the top of the skyscraper. The bottom of the skyscraper is the Right angle.

This forms the right triangle allowing you to find y, the skyscraper height.


, height of the skyscraper.



The next part is the find according to my description, the value for n. The other tutor made a good drawing, otherwise difficult to describe in words.

Look at mananth's drawing. SB + BR = y, using symbolism from both of us. We found the value for y already. If we find the value of SB, then we can find BR, and understand that n=BR.

See the right triangle, one leg of 75, the angle at the left being 45 degree.

.
.
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
BS = 75 tan 45
tan 45 =1
BS = 75

(75+x )= 75 tan 54
75 tan 54 - 75 = x
tan 75 = 0.67
75 *0.67-75 = 28.22m
.

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
I have a problem here that states. There are two buildings (I will call them "nearby building" and "skyscraper") and need to find the height of both buildings.
-What we are told is the distance between them is 75m.
-The angle of elevation from the base of the "nearby building" to the top of the "skyscraper" is 54 degrees.
-The angle of elevation from the roof of the "nearby building" to the top of the "skyscraper" is 45 degrees.
Here is the solution I have came up with, knowing the angle from the "nearby building" to the top of the "skyscraper" and considering the other angle is 36. I need to then find the tan(36).
tan36=75/x
x= 75/tan36
x= 103.2
So the skyscraper would be 103.2 meters tall
For the "nearby building" we would do the same
tan45=75/x
x=75/tan45
x=75
Then find the difference 103.2-75=28.2
The nearby building would then be 28.2 meters tall
I wish I could include the graphic I drew to explain it visually, sorry if I didn't word this well enough to understand. We are also told to round to the nearest tenth.
.

Height of skyscraper:  = 103.2286 m ≈  m

Difference in heights of both buildings:  = 75 m

Height of shorter building: 103.2286 - 75 = 28.2286 ≈  m 

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