Question

If $A=B+C$and the values of $A,BandC$ are $13,12and5$ respectively, then the angle between $AandC$ will be

• A. ${\cos }^{-1}\left(\frac{5}{13}\right)$
• B. ${\cos }^{-1}\left(\frac{13}{12}\right)$
• C. $\frac{\mathrm{\pi }}{2}$
• D. ${\sin }^{-1}\frac{5}{12}$

Answer 1

The correct option is A

${\cos }^{-1}\left(\frac{5}{13}\right)$

Explanation for correct option:

Finding angle between $AandC$.

Given, $A=B+C$ & $A=13,B=12andC=5$

$$\begin{gathered} \sin ce{13}^2={12}^2+5^2 \\ \therefore giventriangleisrightatA \end{gathered}$$

Let angle between $AandCis\alpha$

Therefore, from cosine formulae

$\begin{array}{rcl}Cos\theta & =& \frac{5}{13}\\ \theta & =& {\cos }^{-1}\left(\frac{5}{13}\right)\end{array}$

Hence, correct option is $\left(A\right)$