Question

find ( mangle x ).

write your answer as an integer or as a decimal rounded to the nearest tenth.

( mangle x=square )

Explanation:

Step1: Use the cosine law

The cosine law formula is \( \cos X=\frac{VX^{2}+XW^{2}-VW^{2}}{2\cdot VX\cdot XW} \). Given \( VX = 14 \), \( XW=16 \), and \( VW = 6 \).
Substitute the values into the formula: \( \cos X=\frac{14^{2}+16^{2}-6^{2}}{2\times14\times16} \).
First, calculate the numerator: \( 14^{2}+16^{2}-6^{2}=196 + 256-36=416 \).
Then, calculate the denominator: \( 2\times14\times16 = 448 \).
So, \( \cos X=\frac{416}{448}=\frac{13}{14}\approx0.9286 \).

Step2: Find the angle \( X \)

Since \( \cos X\approx0.9286 \), then \( X=\cos^{-1}(0.9286) \).
Using a calculator, \( X\approx21.8^{\circ} \).

Answer:

\( 21.8 \)