Question Video: Using the Law of Sines to Calculate an Unknown Length | Nagwa Question Video: Using the Law of Sines to Calculate an Unknown Length | Nagwa

# Question Video: Using the Law of Sines to Calculate an Unknown Length Mathematics • Second Year of Secondary School

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For the given figure, π΄π΅ = 3 and π΅πΆ = π. Use the law of sines to work out π. Give your answer to two decimal places.

02:22

### Video Transcript

For the given figure, π΄π΅ is equal to three and π΅πΆ is equal to π. Use the law of sines to work out π. Give your answer to two decimal places.

Letβs begin by adding the given measurements to our triangle. We can see that we have a nonright-angled triangle for which we know the measure of two angles and the length of one side. To find the length of the side labelled π, weβll need to use the law of sines: π over sin π΄ equals π over sin π΅, which equals π over sin πΆ.

Alternatively, that can be written as sin π΄ over π equals sin π΅ over π, which equals sin πΆ over π. We only need to use one of these forms. Since weβre trying to calculate the length of one of the sides, weβll use the first form. It doesnβt particularly matter either way. But by using the first form here, it will minimize the amount of rearranging weβll need to do to solve the equation.

Next, weβll label the sides of the triangle. The side opposite the angle π΄ is already given by the lowercase π. The side opposite the angle π΅ is lowercase π, and the side opposite the angle πΆ is lowercase π. For the law of sines, we usually only need to use two parts. We donβt know the side labelled lowercase π, so weβre going to use π over sin π΄ and π over sin πΆ.

Letβs substitute what we know into this formula. That gives us π over sin 64 is equal to three over sin 31. To solve this equation and work out the value of π, weβll need to multiply both sides by sine of 64. π is therefore equal to three over sine of 31 multiplied by sine of 64.

If we put that into our calculator, we get that π is equal to 5.2353 and so on. Correct to two decimal places, π is equal to 5.24. Notice how there were no units provided in the question, so no units are required in our answer.

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