Question

In triangle abc angle abc = 90 degree and angle acb = 30 degree then find AB : AC

Answer 1

Answer:

$\bf\;AB:AC=1:2$

Step-by-step explanation:

$\textbf{Concept:}$

$\textbf{Sine formula}:$

$\displaystyle\text{ In \triangle{ABC} , }\\\\\bf\frac{a}{sin\;A}=\frac{b}{sin\;B}=\frac{c}{sin\;C}=2R$

$\text{Using sine formula, we get}$

$\frac{BC}{sin\;60}=\frac{AC}{sin\;90}=\frac{AB}{sin\;30}=2R$

$\frac{BC}{\frac{\sqrt3}{2}}=\frac{AC}{1}=\frac{AB}{\frac{1}{2}}=2R$

$\frac{2BC}{\sqrt3}=AC=2AB=2R$

$\implies\;AB=R\;\;and\;\;AC=2R$

$\frac{AB}{AC}=\frac{R}{2R}$

$\frac{AB}{AC}=\frac{1}{2}$

$\implies\bf\;AB:AC=1:2$

Answer 2

GIVEN : (IN ∆ABC)

• Angle ABC = 90°
• Angle ACB = 30°

TO FIND :

• AB : AC = ?

STEP - BY - STEP EXPLANATION :

NOTE –––––»

(REFERS TO THE ATTACHMENT)