Video Transcript
Find the length 𝑎 to one decimal place.
In this question, we are given the lengths of two sides of our triangle together with the included angle, and we need to calculate the length of the third side. In order to do this, we will use the law of cosines. This states that 𝑎 squared is equal to 𝑏 squared plus 𝑐 squared minus two 𝑏𝑐 multiplied by the cos of angle 𝐴. The lowercase letters correspond to the lengths of the sides, whereas the uppercase or capital letter corresponds to the measure of the angle.
Substituting in the values from the diagram whilst leaving out the units, we have 𝑎 squared is equal to 14 squared plus 15 squared minus two multiplied by 14 multiplied by 15 multiplied by the cos of 49 degrees. Typing the right-hand side of this calculation into our calculator gives us 145.4552 and so on. This gives us the value of 𝑎 squared. However, we need to calculate 𝑎. So we need to square root both sides of our equation. This gives us 𝑎 is equal to 12.0604 and so on.
We are asked to give our answer to one decimal place. Therefore, 𝑎 is approximately equal to 12.1. As the units of the lengths of our triangle are kilometers, we can conclude that 𝑎 is equal to 12.1 kilometers to one decimal place.
