Triangle Calculations and Trigonometry

The video tutorial explains how to find the length of a side in a triangle using the law of cosines. It begins by labeling the triangle's angles and sides, then sets up the equation for the law of cosines. Known values are substituted into the equation, which is then simplified. The tutorial demonstrates how to calculate the result using a calculator, ensuring the calculator is in degree mode, and rounds the result to four decimal places.

What is the known angle labeled as in the triangle?

• Angle A

• Angle B

• Angle C

• Angle D

Which side of the triangle is opposite to angle B?

• Side a

• Side b

• Side c

• Side x

What is the formula for the Law of Cosines used in this problem?

• 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

• a^2 = b^2 + c^2 - 2bc cos A

What value is substituted for side b in the equation?

• 18.6

• 40

• 22

• 29

What is the result of 22 squared?

• 484

• 841

• 1276

• 1325

What operation is performed to solve for side a after simplifying the equation?

• Multiplying by 2

• Dividing by cosine

• Taking the square root

• Taking the cube root

Why is it important to ensure the calculator is in degree mode?

• To ensure the calculator is working

• To make the calculator faster

• To avoid errors in trigonometric calculations

• To save battery life

What is the approximate length of side a after rounding?

• 29

• 18.6421

• 18.6

• 22

What is the purpose of rounding the final answer to four decimal places?

• To match the homework requirements

• To make the number smaller

• To make the number larger

• To make the calculation easier

What is the final value of x in the problem?

• 18.6

• 22

• 18.6421

• 29