Question

In triangle XYZ, measure of angle X=152, y=15, z=19. Find x to the nearest thousandth.

Answer 1

In triangle XYZ, measure as shown below

Step 1: Using Cosine rule

`\begin{gathered} x^2=y^2+z^2\text{ - 2yz CosX} \\ x^2=15^2+19^2\text{ - 2(15)(19)Cos 152} \\ x^2=\text{ 225+361-570 cos 152} \end{gathered}`
`\begin{gathered} x^2=\text{ 586-570(-0.88295)} \\ x^2=586\text{ + 503.28} \\ x^2=\text{ 108}9.28 \\ x\text{ = }\sqrt[]{1089.28} \\ x\text{ = 33.004} \end{gathered}`

Hence the value of x = 33.004