# In ∆Abc, If a = 18, B = 24 and C = 30 and ∠C = 90°, Find Sin A, Sin B and Sin C. - Mathematics

In ∆ABC, if a = 18, b = 24 and c = 30 and ∠c = 90°, find sin A, sin B and sin C

#### Solution

Given,∠C = 90°, a = 18, b = 24 and c = 30
According to sine rule, $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

$\Rightarrow \frac{c}{\sin C} = \frac{a}{\sin A}$
$\Rightarrow \sin A = \frac{a\sin C}{c}$
$= \frac{18 \times \sin\left( 90° \right)}{30}$
$= \frac{18}{30}$
$= \frac{3}{5}$
$Also, \frac{b}{\sin B} = \frac{c}{\sin C}$
$\Rightarrow \sin B = \frac{b\sin C}{c}$
$= \frac{24\sin90°}{30}$
$= \frac{24}{30}$
$= \frac{4}{5}$
$and$
$\sin C = \sin90° = 1$

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 10.1 | Q 3 | Page 12