Question

(50 POINTS) What is the length of YZ in Triangle XYZ? Explain two different methods that could be used to find this length.

Answer 1

First Method:

Using cosine rule:

$\rightarrow \sf cos(30 ) = \dfrac{YZ}{12}$

$\rightarrow \sf YZ = 12cos(30 )$

$\rightarrow \sf YZ = 6\sqrt{3}$

$\rightarrow \sf YZ = 10.4$

Second Method:

First find XY using sine rule:

$\rightarrow \sf sin(30)=\dfrac{XY}{12}$

$\rightarrow \sf XY = 12sin(30)$

$\rightarrow \sf XY =6$

Then use Pythagoras Theorem:

⇒ XY² + YZ² = XZ²

⇒ (6)² + YZ² = 12²

⇒ YZ² = 144 - 36

⇒ YZ = √108

⇒ YZ = 6√3

⇒ YZ = 10.4