Introduction to the Cosine Rule for Finding Missing Lengths and Angles in Triangles

Introduction to the Cosine Rule for Finding Missing Lengths and Angles in Triangles

Assessment

Interactive Video

Mathematics

University

Hard

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The video tutorial covers the use of trigonometry in solving problems involving triangles. It begins with an introduction to SohCahToa for right angle triangles and transitions to the cosine rule for non-right angle triangles. The cosine rule is explained in detail, including its derivation and application in finding missing side lengths and angles. The tutorial concludes with practical examples demonstrating how to apply the cosine rule in various scenarios.

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7 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which trigonometric ratio is used to find the opposite side in a right-angle triangle?

Secant

Cosine

Tangent

Sine

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is required to apply the cosine rule to find a missing side?

One side and one angle

Two angles and a side

Two sides and the included angle

All three angles

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the derivation of the cosine rule, which theorem is used to calculate the height of the triangle?

Area Formula

Pythagoras' Theorem

Sine Rule

Law of Tangents

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the formula for the cosine rule when finding a missing side?

a^2 = b^2 + c^2 - 2bc cos A

a^2 = b^2 + c^2 - 2bc sin A

a^2 = b^2 + c^2 + 2bc cos A

a^2 = b^2 - c^2 + 2bc cos A

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When using the cosine rule to find an angle, what must you do with the formula?

Multiply by 2

Rearrange to solve for cos A

Add all sides

Subtract the smallest side

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the example given, what is the missing side length calculated using the cosine rule?

35 kilometers

68 kilometers

90 kilometers

83.46 kilometers

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the angle found using the cosine rule in the example provided?

90 degrees

107.7 degrees

68 degrees

35 degrees