Geometry 8-5 Complete Lesson: Law of Sines

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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.

G.SRT.10

G.SRT.11

G.SRT.10

G.SRT.11

G.SRT.8

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

G.SRT.10

G.SRT.11

Geometry 8-5 Complete Lesson: Law of Sines

Geometry 8-5 Complete Lesson: Law of Sines

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.

Problem 1 Got It?

Problem 2 Got It?

Problem 3 Got It?

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.

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.

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.

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

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.

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.

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.

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.

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

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

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

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?

Reflection: Math Success

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.

Problem 1 Got It?

Problem 2 Got It?

Problem 3 Got It?

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.

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.

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.

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

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.

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.

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.

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.

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

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

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

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?

Reflection: Math Success

Geometry 8-5 Complete Lesson: Law of Sines

Geometry 8-5 Complete Lesson: Law of Sines

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.

Problem 1 Got It?

Problem 2 Got It?

Problem 3 Got It?

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.

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.

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.

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

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.

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.

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.

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.

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

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

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

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?

Reflection: Math Success

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.

Problem 1 Got It?

Problem 2 Got It?

Problem 3 Got It?

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.

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.

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.

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

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.

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.

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.

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.

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

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

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

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?

Reflection: Math Success

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.

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

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.

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