The sides of a triangle are in the ratio 1 : | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the sides of the triangle be $a = k$,$b = \sqrt{3}k$,and $c = 2k$.Since $a^2 + b^2 = k^2 + (\sqrt{3}k)^2 = k^2 + 3k^2 = 4k^2 = c^2$,the triang

Vedclass · Accepted Answer

$1 : 2 : 3$

Vedclass · Answer

(A) Let the sides of the triangle be $a = k$,$b = \sqrt{3}k$,and $c = 2k$.Since $a^2 + b^2 = k^2 + (\sqrt{3}k)^2 = k^2 + 3k^2 = 4k^2 = c^2$,the triangle is a right-angled triangle with the hypotenuse $c = 2k$.Let the angles opposite to sides $a, b, c$ be $A, B, C$ respectively.Then $C = 90^{\circ}$.Using the sine rule or trigonometric ratios in a right triangle:$\sin A = \frac{a}{c} = \frac{k}{2k} = \frac{1}{2} \implies A = 30^{\circ}$.$\sin B = \frac{b}{c} = \frac{\sqrt{3}k}{2k} = \frac{\sqrt{3}}{2} \implies B = 60^{\circ}$.Thus,the angles are $30^{\circ}, 60^{\circ}, 90^{\circ}$.The ratio of the angles is $30^{\circ} : 60^{\circ} : 90^{\circ} = 1 : 2 : 3$.

The sides of a triangle are in the ratio $1 : \sqrt{3} : 2$. Then the angles are in the ratio

Similar Questions

In a triangle,if $b=5, c=6$,and $\tan \frac{A}{2}=\frac{1}{\sqrt{2}}$,then $a=$

If in a $\triangle ABC$,$r_3 = r_1 + r_2 + r$,then $\angle A + \angle B$ is equal to (in $^{\circ}$)

In a $\Delta ABC$,if $A = 30^o$,$b = 2$,and $c = \sqrt{3} + 1$,then $\frac{C - B}{2} = $ ....$^o$

In $\Delta ABC,$ if $(a + b + c)(a - b + c) = 3ac,$ then

In a $\triangle ABC$,$\frac{2(r_1+r_3)}{ac(1+\cos B)} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module