# Angles and Steepness

ID: tahud-dafov
Illustrative Mathematics, CC BY 4.0
Subject: Geometry

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 ﻿$1:12$﻿ ratio for the legs. Select ﻿$\textbf{all}$﻿ 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

##### Problem 2

Find the missing side in each triangle using any method.

2) Find the length of ﻿$AC$﻿.

3) Find the length of ﻿$DE$﻿.

##### 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 ﻿$1:12$﻿ 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 ﻿$AC$﻿ and ﻿$DE$﻿ are parallel, and line ﻿$DC$﻿ is perpendicular to each of them. What is a reasonable estimate for the length of side ﻿$DE$﻿?

Given: ﻿$AC \parallel DE$﻿, ﻿$DC \perp DE$﻿, ﻿$DC \perp AC$﻿

a)

﻿$\frac{1}{3}$﻿

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 ﻿$\sqrt{2}$﻿

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 ﻿$ABC$﻿, the measure of angle ﻿$A$﻿ is ﻿$35\degree$﻿ and the measure of angle ﻿$B$﻿ is ﻿$20\degree$﻿ . In triangle ﻿$DEF$﻿, the measure of angle ﻿$D$﻿ is ﻿$35\degree$﻿ and the measure of angle ﻿$F$﻿ is ﻿$125\degree$﻿.

12) Are triangles ﻿$ABC$﻿ and ﻿$DEF$﻿ similar?

True or false? Write below.

13) Explain or show your reasoning.