Geometry 8-5 Law of Sines

by Matthew Richardson

| 21 QuestionsNote from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

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Solve It! A search-and-rescue boat spots a lost hiker on the edge of a rock shelf. How many feet is the boat from the hiker? Round to the nearest whole foot and enter only a number. Hint: Consider partitioning the triangle into two right triangles.

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Problem 1 Got It?

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Problem 2 Got It?

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Problem 3 Got It?

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Reasoning: If you know the three side lengths of a triangle, can you use the Law of Sines to find the missing angle measures? Explain.

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Error Analysis: In △PQR, PQ = 4 cm, QR = 3 cm, and m∠R = 75. Your friend uses the Law of Sines to write the following proporiton to find m∠P.

Explain your firend's error.

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Review Lesson 8-4: Indirect Measurement: A hot-air balloon pilot sights the landing field from a height of 2000 ft. The angle of depression is 24°. Create an illustration to model the scenario on the canvas. Remember that you can upload images to the canvas. Label all know quantities and relevant information.

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Review Lesson 8-4: Refer to your work in the previous item. To the nearest foot, what is the ground distance from the hot-air balloon to the landing field? Enter only a number.

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Review Lesson 4-5: What is the value of x? Enter only a number.

You may use the embedded Desmos scientific calculator below for the Mixed Review items that follow.

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Review Lesson 8-3: Evaluate the expression. Round your answer to the nearest hundredth. Include a 0 placeholder in the ones place, if needed. Enter only a number.

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Review Lesson 8-3: Evaluate the expression. Round your answer to the nearest hundredth. Include a 0 placeholder in the ones place, if needed. Enter only a number.

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Review Lesson 8-3: Evaluate the expression. Round your answer to the nearest hundredth. Include a 0 placeholder in the ones place, if needed. Enter only a number.

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Vocabulary Review: Draw a line segment from each angle of the triangle to its opposite side.

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Vocabulary Review: A ratio is the comparison of two quantities by __?__.

addition

subtraction

multiplication

division

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Use Your Vocabulary: A triangle has a given acute angle. What is its sine ratio?

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Use Your Vocabulary: A right triangle has one acute angle measuring 36.9°. The length of the side adjacent to the angle is 4 units, and the length of the side opposite this angle is 3 units. The length of the hypotenuse is 5 units. What is the sine ratio if the 36.9° angle?

4/3

3/5

5/4

5/3

4/5

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Reflection: Math Success

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