Subject: Mathematics    / Geometry

Question
Right Triangles and Trigonometry Portfolio GEOMETRY B Directions: The ADA (American with Disabilities act) requires specific building codes for wheelchair ramps. This applies to both businesses and home construction. For this portfolio entry you will research and investigate wheelchair ramps and their connections to Geometry and Trigonometry. 1. Name at least two places in your community where you have seen wheelchair ramps. 2. Research the ADA’s requirements for wheelchair ramps. What is the acceptable slope ratio for a wheelchair ramp? Explain, in your own words, what this ratio means. 3. Find a wheelchair ramp either online or in your community. You can take a picture of one (state where your wheelchair ramp is from) and paste it in your portfolio. If you find one online, make sure to cite from where you are taking the picture. 4. Sketch over the right triangle formed from your wheelchair ramp and the ground. Include the lengths of each side of the triangle in your sketch. 5. Use the Converse of the Pythagorean Theorem to verify that the measurements of your wheelchair ramp are consistent with those of a right triangle (Hint: Show that ). Show all work. If the measurements are not consistent, explain why you think this may be. 2 22 c = + a b 6. Label the angle formed between the ground and the wheelchair ramp ?A. Write hypotenuse along the hypotenuse, adjacent side along the leg adjacent to ?A, and opposite leg along the leg opposite of ?A. 7. Write the sine, cosine, and tangent ratios for ?A. 8. Reduce the tangent ratio of ?A. Is this ratio in compliance with the building code slope ratio for wheelchair ramps? Explain why or why not. 9. Find the measure of ?A using inverse tangent. Show all work. 10.In conclusion, explain in at least two sentences how mathematics plays an important role in making sure ramps are safe and easy to use.

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