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Trigonometric Ratios by Amy H. This PowerPoint presentation was made by one of my 7 th grade honors students. The assignment was to demonstrate the steps in solving a trigonometry problem of her choice.
The Question <ul><li>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 . </li></ul><ul><li>To the nearest 100 feet, how far above the ground are the lights? </li></ul>
Choose a Trig Function <ul><li>SINE of 5 </li></ul><ul><li>COSINE of 5 </li></ul><ul><li>TANGENT of 5 </li></ul>To calculate the height of the lights at the top of the building.
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. 2 miles 5 ?? X
Set-up of the Equation TAN of 5 = X 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… TAN of 5 = X 10,560 ft.
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. TAN of 5 = X 10,560 ft. Now becomes……… .08749 = X 10,560 ft.
Isolate the variable Multiply both sides of the equation by 10,560. .08749 = X 10,560 ft. (10,560) (10,560) Now becomes……… 923.8944 = X
Solution 923.8944 = X The question requested that the answer be rounded to the nearest 100 feet. Therefore… 923.8944 = 900 feet
Conclusion The building lights are about 900 feet above the ground. 2 miles 5 ?? 900