# In ∆ Abc, If a = 18, B = 24 and C = 30, Find Cos A, Cos B and Cos C. - Mathematics

In ∆ ABC, if a = 18, b = 24 and c = 30, find cos A, cos B and cos C

#### Solution

$\text{ Given }: a = 18, b = 24 \text{ and } c = 30 .$

$\cos A = \frac{b^2 + c^2 - a^2}{2bc} = \frac{576 + 900 - 324}{2 \times 24 \times 30} = \frac{1152}{1140} = \frac{4}{5}$

$\cos B=\frac{a^2 + c^2 - b^2}{2ac}=\frac{324 + 900 - 576}{2 \times 18 \times 30}= \frac{648}{1080} =\frac{3}{5}$

$\cos C=\frac{a^2 + b^2 - c^2}{2ab}=\frac{576 + 324 - 900}{2 \times 24 \times 18}=0$

Hence, $\cos A = \frac{4}{5}, \cos B=\frac{3}{5}, \cos C= 0$

Concept: Sine and Cosine Formulae and Their Applications
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 10 Sine and cosine formulae and their applications
Exercise 10.2 | Q 4 | Page 25