In triangle XYZ, |XY| = 10cm, |YZ| = 9 cm and |XZ| = 7 cm. If XZY = \(\alpha\), find the value of cos \(\alpha\).
- \(\frac{11}{15}\)
- \(\frac{17}{35}\)
-
\(\frac{5}{21}\)
- \(\frac{7}{32}\)
The correct answer is: C
Explanation
Using, cos \(\alpha\) = \(\frac{ b^2 + c^2 - a^2}{2bc}\)
cos \(\alpha\) = \(\frac{ 9^2 + 7^2 - (10)^2}{2 \times 9 \times 7}\)
= \(\frac{ 130 - 100}{126}\) = \(\frac{30}{126}\) = \(\frac{5}{21}\)