Question

$\huge\color{pink}\mathfrak{Answer}$

$\sf{In TRIANGLE ABC cos \: C = \frac{12}{13} and \:BC = 24 \: then \: AC =?}$


Answer it ASAP PLZ ​

Answer 1

In ∆ABC right angle at B

and for angle C

• Height = AB
• Base = BC = 24 cm
• Hypotenuse = AC

and we know that,

$\: \: \: \: \: \: \: \: \: \: \bold{cos \theta = \frac{base}{hypotenuse} } \\ \\ \bold{: \implies cos \:C = \frac{base}{hypotenuse} } \\ \\ \bold{: \implies \: cos \:C = \frac{BC}{AC} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

but it is given that

$\bold{cos \: C = \frac{12}{13}} \\ \\ \bold{: \implies \frac{BC}{AC} = \frac{12}{13} } \\ \\ \bold{: \implies \frac{24}{AC} = \frac{12}{13} } \\ \\ \bold{ : \implies \frac{24}{12} = \frac{AC}{13} } \\ \\ \bold{: \implies \frac{AC}{13} = \cancel\frac{24}{12} } \\ \\ \: \: \: \: \: \: \bold{: \implies \: AC = 2 \times 13 } \\ \\ \bold{: \implies AC = 26 } \: \: \:$

so, AC = 26 cm