Question

In ∆ABC, If Angle A=45°, Angle B = 60° then find the ratio of its sides.​

Answer 1

Pls mark as brainliest answer

Answer 2

Answer:

$a:b:c </p><p>= 2 : \sqrt{6} : ( \sqrt{3} + 1) \:$

Step By Step Explanation:

By the sine rule,

$\frac{a}{ \sin(a) } = \frac{b}{ \sin(b) } = \frac{c}{ \sin(c) }$

$\frac{a}{b} = \frac{ \sin \: a } { \sin \: b} \: \: and \: \: \frac{b}{c} = \frac{ \sin \: b } { \sin \: c}$

$a : b : c = \sin \: a: \sin \: b \: : \sin \: c \:$

Given:

Angle A =45°

Angle B=60°

→ Angle A + Angle B + Angle C = 180°

45°+60°+Angle C=180°

Angle C =180°-105°

Angle C = 75°

Now,

→ Sin A = Sin 45° =

$\frac{1}{ \sqrt{2} }$

→ Sin B = Sin 60° =

$\frac{ \sqrt{3} }{2}$

→ Sin C

= Sin 75°

= Sin(45°+30°)

=Sin 45° Cos 30° + Cos 45° Sin 30°

$= \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} + \frac{1}{ \sqrt{2} } \times \frac{1}{2} \\ = \frac{ \sqrt{3} }{2 \sqrt{2} } + \frac{1}{2 \sqrt{2} } \\ = \frac{ \sqrt{3} + 1} {2 \sqrt{2} }$

→ The Ratio of the sides of ∆ ABC

= a:b:c

→ $a:b:c = 2 : \sqrt{6} : ( \sqrt{3} + 1)$

→ $a:b:c = 2 : \sqrt{6} : ( \sqrt{3} + 1) \:$

→ Sin A : Sin B : Sin C

$= \frac{1}{ \sqrt{2} } : \frac{ \sqrt{3} }{2} : \frac{ \sqrt{3} + 1 }{2 \sqrt{2} }$

→ $a:b:c </p><p>= 2 : \sqrt{6} : ( \sqrt{3} + 1) \:$