Imagine a diagram depicting this problem. On the diagram is a line drawn from the *bottom* of the building to a point on the ground exactly 1 mile away. There is also a line drawn from the *top* of the building to that same point. A triangle is formed by the two lines and the wall of the building.
From that single point are two lines branching out to form an angle, a.k.a. the angle of elevation.
The angle of elevation is given as 11 degrees. I am assuming you are learning about sin, cosine, and tangent; you can solve the equation using just one of these functions.
The question is asking you to find the height of the building. If you think of this problem like a triangle, you are literally finding the height of the triangle. The height of the triangle is going to be opposite to the angle of elevation. The base of the triangle, or the bottom, is known to be 1 mile.
Sin = opposite/hypotenuse
Cos = adjacent/hypotenuse
Tan = opposite/adjacent
These functions can help us calculate the relationships between side lengths and angle values.
"Adjacent" refers to a side length touching your angle. 1 mile is a side length that touches the 11 degree angle of elevation. Because we are dealing with opposite and adjacent, we can use tan to solve our problem.
Pair tan with your given angle.
Tan11 = [tex] \frac{x}{1mile} [/tex]
We are trying to get x by itself, because it represents the opposite length, a.k.a. the height of the building.
Use your calculator (or website) to find the inverse of tan11 degrees . Make sure you are calculating in degrees.
inverse tan11 degrees times 1 mile = [tex] \frac{x}{1mile} [/tex] times 1 mile
Multiply both sides by the denominator to get x by itself.
If you calculate correctly, you should get 0.19438031 as an answer. Therefore, the height is 0.19438031 times the base length. 1 mile, or 5,280 feet times 0.19438031 roughly equals 1026.33 feet. Or, the answer could simply be 0.19438031 miles.
