Solving Triangles with Law of Sines

This video tutorial explains how to find the length of a side in a non-right triangle using the Law of Sines. It begins by introducing the problem and the known values, then explains the Law of Sines and how to apply it. The tutorial walks through setting up and solving the equation for the unknown side length, x, using algebraic manipulation. It also provides guidance on using a calculator to compute the final value, ensuring the calculator is in degree mode and rounding the result to four decimal places. The tutorial concludes with a summary of the steps taken.

What is the main goal of the problem discussed in the video?

• To calculate the perimeter of the triangle

• To determine the length of side x

• To find the measure of angle C

• To find the area of the triangle

Which mathematical principle is used to solve for side x?

• Pythagorean Theorem

• Law of Cosines

• Trigonometric Identities

• Law of Sines

What is the length of side a in the triangle?

• 63 units

• 24 units

• x units

• 11 units

How is the equation set up using the Law of Sines?

• sine 24 degrees / x = sine 63 degrees / 11

• sine 63 degrees / x = sine 24 degrees / 11

• sine 63 degrees / 11 = sine 24 degrees / x

• sine 24 degrees / 11 = sine 63 degrees / x

What is the significance of the number 11 in the equation?

• It is the measure of angle B

• It is the length of side a

• It is the measure of angle A

• It is the length of side b

What is the first step in solving the equation for x?

• Subtract 11 from both sides

• Add 11 to both sides

• Multiply both sides by 11x

• Cross multiply

What operation is performed to isolate x in the equation?

• Multiply by sine 63 degrees

• Divide by sine 24 degrees

• Add sine 24 degrees

• Subtract sine 63 degrees

What should you ensure about the calculator before calculating the value of x?

• It is in degree mode

• It is in radian mode

• It is in scientific mode

• It is in standard mode

What is the rounded value of x to four decimal places?

• 24.0970

• 24.0968

• 24.0967

• 24.0969

Why is it important to use parentheses when entering the quotient in the calculator?

• To make the equation look neat

• To ensure the correct order of operations

• To separate the numerator and denominator

• To avoid syntax errors