This week, my biggest mistake in math was using the Cosine Law when I should have used the Sine Law. I had been given two angles and one side (AAS), but I had forgotten that Cosine Law is used in different types of triangle problems. This gave a confusing and wrong answer.
-Question with Mistake
The question was:
“In triangle ABC, angle A = 40°, angle B = 65°, and side a = 10 cm. Find side b.”
I wrongly tried to use the Cosine Law:
b^2 = c^2 + a^2 – 2ac x Cos(B)
But I didn‘t even have side c, so I was trying to put in values I didn‘t have. I got stuck and ended up guessing or doing wrong calculations.
Here is what I should done with Sine law:
First I would need to find the angle C:
C = 180 – 140 – 65 = 75
Now I needed to use Sine law:
Now I need to solve for b by cross multiplying, then isolating b:
Then by solving I would get the answer:
-What I Learned
I discovered that Cosine Law will only function if you are given SAS (two sides and the included angle) or SSS (three sides). In this problem, I was given AAS (two angles and a side), so Sine Law was the way to go. I also discovered the importance of checking what information I’m given before jumping into a formula. Spending more time and thinking carefully about what is familiar to me can avoid making such errors in the future.