The document is a student's presentation summarizing the steps to solve a trigonometry problem about determining the height of lights on a building from an observer's perspective. The presentation shows setting up the tangent ratio equation using the given information of the observer being 2 miles from the building at a 5 degree angle of elevation. The student uses trigonometric functions to isolate and solve for the variable, determining the height of the lights is approximately 900 feet above the ground.

1. 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.

3. Picture the Problem 2 miles 5  X

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. 2 miles 5  ?? X

6. 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.

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. TAN of 5  = X 10,560 ft. Now becomes……… .08749 = X 10,560 ft.

8. 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

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. 2 miles 5  ?? 900