The Law of Sines states that for any triangle the ratio between the sine value of an angle and the length of its opposite side is constant.
See solution.
Practice makes perfect
We are asked to describe and correct the error made in finding m∠C. Let's start by recalling the Law of Sines.
Law of Sines
For any triangle, the ratio between the sine value of an angle and the length of its opposite side is constant.
Next let's identify which sides of △ ABC are opposite to ∠A and ∠C.
We can see that side BC is opposite ∠A, and side AB is opposite ∠C. According to the Law of Sines, the ratio of the sine of ∠C to the length of AB is equal to the ratio of the sine of ∠A to the length of BC.
sinC/AB=sinA/BC
Let's substitute 55^(∘) for A, 5 for AB, and 6 for BC.
sinC/5=sin55^(∘)/6
We can see that the obtained expression is different from the given one.
& Our Expression &Given Expression
&sinC/5=sin55^(∘)/6 &sinC/6≠sin55^(∘)/5
The denominators of the ratios have been switched. Finally, let's correct the error. We will use our equation to find the measure of ∠C.
