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Hi, Peter!
A
Hey, Ella! Can you help me analyze a problem?
Sure. What is it about?
A
What is the height of a building with an angle of elevation of 60 degrees at a distance of 60 m from its foot?
Hmm. That's easy.
A
Can you teach me how?
B
Let's use this building as a reference.  Here, AB represents height of the building, BC represents distance of the building from the point of observation.
60 m
60°
C
B
In the right triangle ABC, the side which is opposite to the angle 60° is known as opposite side (AB), the side which is opposite to 90° is called hypotenuse side (AC) and the remaining side is called adjacent side (BC).Now we need to find the length of the side AB.
60 m
60°
C
B
To solve this, we are going to use the formula, tanθ = Opposite side/Adjacent side. Since we have 60°, our tanθ will be tan60°. tan60° is equal to √3. √3  = AB/BC.  Side BC will be replaced with 60 so the equation will be √3 = AB/60. In order to find the measurement of side AB, you should transpose 60 to the other side so the resulting equation will be √3 x 60 = AB. The approximate value of √3 is 1.732. Therefore AB = 60 (1.732). AB is 103.92 m. So, the height of the building is 103.92 m.
60 m
60°
C

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