If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Precalculus

### Course: Precalculus>Unit 2

Lesson 4: Law of sines

# Solving for an angle with the law of sines

Sal is given a triangle with two side lengths and one angle measure, and he finds all the missing angle measures using the law of sines. Created by Sal Khan.

## Want to join the conversation?

• At , why do we take the inverse sine instead of dividing both sides by sine to get rid of the sine of the right side?
• You can't divide the sines of two different angles. On scene , our angles are theta and 40 degrees. Although dividing by sin(theta) would remove the sine from the right side, you would only be left dividing the sine of 40 degrees and the sine of theta on the left side. However, you can use inverse sine and remove the sines that way, because the inverse sine of the sine of 40 degrees is 40 degrees and the inverse sine of the sine of theta is theta.
• I didn't understand the inverse sin step. Can anyone please explain to me what it is?
• The inverse sin gets him to theta by itself
• Is there a Law Of Tangents?
• Yes there is. The Law of Tangents is a statement involving the tangents of two angles in a triangle and the lengths of opposite sides.

The Law of Tangents state:
a-b/a+b = tan[1/2(A-B)]/tan[1/2(A+B)]
• If you search the law of sines on the internet, it'll mostly give you A/sin(a) = B/sin(b) = C/sin(c). But, to find a missing angle, it's best to use sin(a)/A = sin(b)/B = sin(c)/C. Is there a way to use
A/sin(a) = B/sin(b) = C/sin(c) to find a missing angle?
• If you have A/sin(a) = B/sin(b), you can just solve for the angle using Algebra.
A = B * sin(a) / sin(b)
A * sin(b) / B = sin(a)
a = arcsin(A * sin(b) / B)
• Hi, I have a question. I have an hp35s calculator.
1. I did the following question on law of sines-
sin14°13'36"/803.94=sinX/1879.28
I get the answer 35°03'48". Which is correct, but the answer could also be 144°56'12". Why is that? I only ask because a question I was doing required me to know that.
2.Your example of the law of sines.
sin40/30=sinx/40
I got an answer of 58°59'13"
I think I did this as precise as I could because the question I did above came out correctly and is the same format. I'm sure you weren't getting into that precise of an answer, but in my situation, I must have it that precise for a test. So, my question for this one- would my answer be correct in terms of pricision?

Thank you,

Jerry
• 145 degrees is just the same as 35 degrees but pointing in the opposite direction. The vertical height of the triangle is the same.
• What is the difference between degree mode and radian mode? Thanks
• You said mode in your question, so I suppose you are refering to calculators. Degree mode will set up your calculator to work with degrees.So in any operation that involves an angle amplitude or trig ratio, your results will be in degrees. In radian mode, your calculator will set up to work with radians, that means, a different unit of amplitude. Always remember to switch modes acordingly to the unit you are using, else you will get some pretty weird answers.

Hope this helps.
• Does it matter that much at whether a capital "A" is used or a lowercase "a" is used in the low of sines.

Example; sinA/a= sinB/b=sinC/c if the triangle angle are the capital 'A"'s
• Nope- the letters don't matter- they only stand for words. as long as the values are being divided correctly (AKA, the angle of sine are divided by the corresponding side length), you could call one angle "Marshmallow" and another angle "Cheeseburger" and it wouldn't make one smidgeon of a difference.
• I'm not sure if this is just another way to do it, or it worked this once by luck, but about into the video I paused it because something clicked when he was talking about the constant ratio between all sides and angles in a triangle, and I immediately went to google calculator, found the constant ratio, multiplied it by 40(the measure of the side, not the angle) and then did the inverse sine of that, and I unpaused the video to see if I got it correct(I did). Will this always work?
• 👍Of course, it is right! you can test this in the practice btw! This is pure genius since you put it constant ratio. Great Job!

Hope this helped you understand and get encouraged!

#YouKhanLearnAnything.💪