Question

Choose the correct Law (Law of Cos or Law of Sin) to solve for x in the given triangle. Show your work! In Triangle ABC, the measure of angle A = 34, AC = 10 and AB = 12. Find BC which is x.

Answer 1

Solution

Step 1

Write the cosine formula for the given triangle.

$a^2\text{ = c}^2\text{ + b}^2\text{ - 2cbcosA}$

Step 2

Write the given data

$\begin{gathered} A\text{ = 34. b = 10, c = 12, a = x} \\ x^2\text{ = 12}^2\text{ + 10}^2\text{ - 2}\times12\times10cos34 \\ x^2\text{ = 144 + 100 - 240}\times0.82904 \\ x^2\text{ = 244 - 198.9690174} \\ x^2\text{ = 45.03098259} \\ \text{x = }\sqrt{45.03098259} \\ \text{x = 6.71} \end{gathered}$

Final answer

x = 6.71