SOLUTION: Can you please help me solve this: You have collected data on several buildings. For each building, you are given the angle of the line of sight up to the top of the building, and

Question 75258: Can you please help me solve this: You have collected data on several buildings. For each building, you are given the angle of the line of sight up to the top of the building, and the distance to the building. Calculate the height of each building.
Building 4 Angle 5� Distance 47.22 meters

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
I think you have posted several problems of this type. Each can be solved using the procedures
that we will use in this problem.
.
This is a trigonometry problem. It involves a right triangle which you need to visualize like
this.
.
Put a spot on the ground 47.22 meters away from the building. The building is perpendicular
to the ground and by definition this means the building and the ground form a right angle.
From the top of the building if you draw a line that connects to the spot on the ground, this
line will be the hypotenuse of the right triangle because it is opposite the 90 degree angle
that the building forms with the ground.
.
There are two legs to this right triangle. One of the legs is the 47.22 meters between the
spot on the ground and the base of the building. The other leg is the height of the building.
.
The height of the building is the side opposite the 5-degree angle formed by the hypotenuse and
the distance along the ground between the spot and the base of the building. The side adjacent
to the 5 degree angle is the 47.22 meter length from the spot to the base of the building.
.
This problem is best solved by using the Tan (tangent) function. Tan is defined as:
.

.
A is 5 degrees.
.
In this equation we know two of three things. We know that the angle A is 5 degrees.
And we know that the adjacent side of the angle is 47.22 meters.
.
Substitute these two values and we get:
.

.
We can use a scientific calculator to get the Tan of 5 degrees. If you do that you find
that the tangent of 5 degrees is 0.087488663
.
Substitute that value and the equation becomes:
.

.
Multiply both sides by 47.22 to get rid of the 47.22 in the denominator of the right side and
the result is
.

.
This means that the opposite side (which is the height of the building) equals the product
of 0.087488663 and 47.22. Multiply this out and the building height (that is the opposite
side) is 4.1313 meters.
.
Hope this pattern helps you to work the rest of the problems you submitted. You will need the
tangent function for them all. Just change the angle and the adjacent side (the distance to
the building) as called for in the other problems.
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