Angles and Steepness

ID: tahud-dafov
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Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Geometry
Grade: 9-12
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13 questions

Angles and Steepness

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Problem 1

1) The Americans with Disabilities Act states that ramps must have an angle less than or equal to 4.8 degrees. Remember, a 4.8 degree angle in a right triangle has a 1:121:12 ratio for the legs. Select all\textbf{all} ramps that meet the Americans with Disabilities Act requirements. Write each corresponding letter in the answer box and separate letters with commas.

a) Ramp A \quad\quad b) Ramp B \quad\quad c) Ramp C \quad\quad d) Ramp D \quad\quad e) Ramp E

A template for answering this question. Ask your instructor for an alternative.
Problem 2

Find the missing side in each triangle using any method.

A template for answering this question. Ask your instructor for an alternative.

2) Find the length of ACAC.

3) Find the length of DEDE.

Problem 3

4) The Americans with Disabilities Act states that ramps must have an angle less than or equal to 4.8 degrees. Remember, a 4.8 degree angle in a right triangle has a 1:121:12 ratio for the legs. Describe 2 ramps that meet the Americans with Disabilities Act requirements.

Problem 4

5) Kiran is visiting the Statue of Liberty. He wants to test the mirror method of indirect measurement for calculating heights. He is 5.8 feet tall and knows that the Statue of Liberty is 305 feet tall. Sketch a diagram showing where a mirror could be placed to use similar triangles to verify the height of the Statue of Liberty. Make sure to include the distance from Kiran to the mirror and the distance from the mirror to the Statue of Liberty.

Problem 5

6) In this diagram, lines ACAC and DEDE are parallel, and line DCDC is perpendicular to each of them. What is a reasonable estimate for the length of side DEDE?


Given: ACDEAC \parallel DE, DCDEDC \perp DE, DCACDC \perp AC

A template for answering this question. Ask your instructor for an alternative.
a)

13\frac{1}{3}

b)

1

c)

3

d)

6

Problem 6

Lin says she has memorized the lengths of a few right triangles, for example, 3, 4, and 5. She is trying to compile a list of several right triangles but needs your help. Check each set of three lengths below. Answer "true" if the lengths form a right triangle and "false" if they do not.

7) 1, 1, and 2\sqrt{2}

True or false? Write below.

8) 4, 5, and 6

True or false? Write below.

9) 5, 12, and 13

True or false? Write below.

10) 7, 8, and 24

True or false? Write below.

11) 8, 15, and 17

True or false? Write below.
Problem 7

In triangle ABCABC, the measure of angle AA is 35°35\degree and the measure of angle BB is 20°20\degree . In triangle DEFDEF, the measure of angle DD is 35°35\degree and the measure of angle FF is 125°125\degree.

12) Are triangles ABCABC and DEFDEF similar?

True or false? Write below.

13) Explain or show your reasoning.