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9-12 Geometry Unit 7 Lesson 13

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Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 •Lesson 13 Lesson 14

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Unit 7, Lesson 13

Using Radians

Geometry

Practice

Problem 1

Find the length of an arc with a central angle of \(\frac{2\pi}{3}\) radians and a radius of 6 units.
Find the length of an arc with a central angle of \(\frac{5\pi}{6}\) radians and a circumference of 12 units.
Find the measure (in radians) of a central angle of an arc with length 4 units and radius 3 units.

Problem 2

A circle has radius 10 units. For each angle measure, find the area of a sector of this circle with the given measure as its central angle.

\(\frac{\pi}{8}\) radian
\(\frac{3\pi}{4}\) radians
1 radian
2 radians

Problem 3

Each circle has a shaded sector with a central angle measured in radians. What fraction of the circle is each sector?

<p>A circle with shaded sector with a central angle labeled pi over 2. </p> — Circle A

<p style="text-align:justify">A circle with shaded sector with a central angle labeled pi over 12.</p> — Circle B

<p>A circle with shaded sector with a central angle labeled 5 pi over 6.</p> — Circle C

Problem 4

ForLesson 12: Radian Sense

Find the radian measure of each angle.

30 degrees
45 degrees
50 degrees

Problem 5

ForLesson 12: Radian Sense

Find the degree measure of each angle.

\(\frac{\pi}{3}\) radians
\(\frac{\pi}{2}\) radians
\(\frac{3\pi}{4}\) radians
3 radians

Problem 6

ForLesson 11: A New Way to Measure Angles

Calculate the radian measure of a 225-degree angle. Use any method you like, including sketching in the circle diagram provided. Explain or show your reasoning.

<p>Circle with radius 1 unit.</p>

Problem 7

ForLesson 10: Angles, Arcs, and Radii

<p>Circle, 10 centimeter radius. 270 degree sector shown.</p> — Andre’s circle

<p>A circle, radius 5 cm. A 270 degree sector is noted.</p> — Diego’s circle

Andre and Diego are each saving money. They each hope to save 500 dollars. They are tracking their progress on the circles in the images.

Diego thinks that Andre has saved more money than Diego has saved. Andre thinks they have saved the same amount. Do you agree with either of them? Explain or show your reasoning.

Problem 8

ForLesson 5: Triangles in Circles

Clare missed class, and Jada is teaching her how to construct the circumscribed circle of a triangle. Here are the instructions Jada wrote.

“Construct all three perpendicular bisectors of the triangle’s sides. The point where the perpendicular bisectors intersect is called the ‘circumcenter.’ Construct a circle centered at the circumcenter with radius set to the distance between the circumcenter and a vertex. If the triangle has a circumscribed circle, the circle you construct will go through all three vertices.”

Do you agree with Jada’s instructions? Explain your reasoning.