Question

In ∆abc if a=5 , b= 10 and A=30° then angle B and C

Answer 1

Step-by-step explanation:

use formula    cosA =b²+c²-a²/2bc   ,  cosB = a²+c²-b²/2ac  , cosC= a²+b²-c²/2ab

firstly find side c with the help of cosA

cos30°= 100-25+c²/2×10×c  ⇒c²-10√3+75=0  ⇒c =5√3   similarlly

cosB = 25+75-100/2 ×5×5√3   ⇒B = 90° because cos90°=0

cosC = 25+100-75/2×50

cosC = 1/2

  C = 60°   because cos60°= 1/2

angle B =90°   and angle C = 60°

Answer 2

∠ B = 90° and  ∠ C = 60°

Step-by-step explanation:

Given,

a = 5, b = 10 and ∠ B = 30°

To find, the values of ∠ B and ∠ C = ?

We know that,

$\dfrac{a}{\sin A} =\dfrac{b}{\sin B}$

⇒ $\sin B =\dfrac{b}{a}\times \sin A$

Put a = 2, b = 3 and ∠ B = 30°, we get

$\sin B =\dfrac{10}{5}\times \sin 30$

⇒ $\sin B =2\times \dfrac{1}{2}$

⇒ $\sin B =1$

⇒ $\sin B$ = $\sin 90$

Equating both sides, we get

∠ B = 90°

∵ In ∆ABC,

∠ A + ∠ B + ∠ C = 180°

⇒ 30° + 90 ° + ∠ C = 180°

⇒ ∠ C = 180° - 120° = 60°

∴  ∠ B = 90° and  ∠ C = 60°