Algebra and Trigonometry: Non-Right Triangles and Law of Cosines

This video tutorial covers the law of cosines and its application in solving non-right triangles. It includes examples of using the law of sines and Heron's formula for calculating areas. The tutorial also explores complex triangle problems and real-world applications of trigonometry. Advanced techniques in trigonometry and geometry are discussed, providing a comprehensive understanding of these mathematical concepts.

What is the primary condition for using the Law of Cosines?

• When the triangle is a right triangle

• When the triangle is an equilateral triangle

• When the triangle is a non-right triangle

• When the triangle has all sides equal

Tags

CCSS.6.G.A.1

In Heron's formula, what does 's' represent?

• The height of the triangle

• The semi-perimeter of the triangle

• The sum of all sides

• The area of the triangle

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which formula is used to find an unknown angle when all sides of a triangle are known?

• Heron's Formula

• Law of Cosines

• Pythagorean Theorem

• Law of Sines

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the first step in solving for an unknown side using the Law of Cosines?

• Using the Pythagorean Theorem

• Setting up the equation with known sides and angle

• Cross-multiplying the sides

• Finding the semi-perimeter

Tags

CCSS.6.G.A.1

How do you calculate the area of a triangle using Heron's formula?

• By using the Law of Sines

• By using the Law of Cosines

• By using the height and base

• By using the semi-perimeter and side lengths

Tags

CCSS.6.G.A.1

What is the value of S when the sides of a triangle are 4.3, 2.6, and 1.9?

• 3.5

• 4.4

• 4.1

• 3.9

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CCSS.HSG.CO.C.11

In a parallelogram with sides 11 feet and 17 feet, and a longer diagonal of 22 feet, what is the length of the shorter diagonal?

• 21.4 feet

• 20.1 feet

• 19.2 feet

• 18.3 feet

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CCSS.3.MD.D.8

What is the perimeter of a regular octagon inscribed in a circle with a radius of 8 inches?

• 48.98 inches

• 47.89 inches

• 45.67 inches

• 50.12 inches

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

How far apart are two boats after two hours if one travels at 18 mph at a heading of 327 degrees and the other at 4 mph at a heading of 60 degrees?

• 40.5 miles

• 37.3 miles

• 35.2 miles

• 39.1 miles

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CCSS.HSG.SRT.D.9

What is the area of a triangular piece of land with sides 30 feet, 42 feet, and an included angle of 132 degrees?

• 480 square feet

• 468 square feet

• 450 square feet

• 490 square feet

Tags

CCSS.HSG.SRT.D.9