1. Trigonometric Ratios
This PowerPoint
presentation was
made by one of my
honors students. The
assignment was to
demonstrate the
steps in solving a
trigonometry problem
of her choice.
2. The Question
• Suppose you are standing 2 miles away from a tall
building and you see the lights on top of the building.
The angle of elevation from you to the lights is 5°.
• To the nearest 100 feet, how far above the ground
are the lights?
4. Choose a Trig Function
• SINE of 5°
• COSINE of 5°
• TANGENT of 5°
To calculate the height of the lights at the top of the building.
5. The Choice
The only Trigonometric ratio that will work with the
given information is the TAN of 5°. The tangent is
the choice when the hypotenuse measure is
missing.
5°
??
X
2 miles
6. Set-up of the Equation
X
TAN of 5° =
2 miles
First, convert the 2 miles into feet (2 X 5,280) because the
answer is needed to be to the nearest 100 feet. Now the
equation becomes…
X
TAN of 5° =
10,560 ft.
7. Function Translation
Convert the TAN of 5° into a decimal using a
calculator or a function chart. I choose to use Mr.
Rollo’s function chart for my conversion.
X
TAN of 5° =
10,560 ft.
Now becomes………
X
.08749 =
10,560 ft.
8. Isolate the variable
Multiply both sides of the equation by 10,560.
X
(10,560) .08749 = (10,560)
10,560 ft.
Now becomes………
923.8944 = X
9. Solution
923.8944 = X
The question requested that the answer be
rounded to the nearest 100 feet. Therefore…
923.8944 = 900 feet
10. Conclusion
The building lights are about
900 feet above the ground.
900
5°
??
2 miles
