Question

in triangle ABC, AB=90° ,Angle A.=30°,Angle c=60°,AC=14,find AB​

Answer 1

Answer:

$\boxed{\red{\sf\:AB\:=\:7\:\sqrt{3}\:units}}$

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

In $\sf\:\triangle\:ABC$,

$\sf\:\angle\:A\:=\:30^{\circ}\\\\\sf\:\angle\:B\:=\:90^{\circ}\\\\\sf\:\angle\:C\:=\:60^{\circ}\:\:\:\:[\:Given\:]$

$\therefore\sf\:\triangle\:ABC\:is\:a\:30^{\circ}\:-\:60^{\circ}\:-\:90^{\circ}\:triangle.$

$\therefore$ By $30^{\circ}\:-\:60^{\circ}\:-\:90^{\circ}$ triangle theorem,

$\sf\:AB\:=\:\frac{\sqrt{3}}{2}\:AC\:\:\:-\:-\:[\:Side\:opposite\:to\:60^{\circ}\:]\\\\\implies\sf\:AB\:=\:\frac{\sqrt{3}}{2}\:\times\:14\\\\\implies\boxed{\red{\sf\:AB\:=\:7\:\sqrt{3}\:units}}$

Additional Information:

1. $30^{\circ}\:-\:60^{\circ}\:-\:90^{\circ}$ triangle theorem:

The theorem by which the sides of a right angled triangle with other two angles of $30^{\circ}\:-\:60^{\circ}$ respectively, can be calculated is called as $30^{\circ}\:-\:60^{\circ}\:-\:90^{\circ}$ triangle theorem.

2. Side opposite to $30^{\circ}$:

The side opposite to $30^{\circ}$ is always half of the hypotenuse.

3. Side opposite to $60^{\circ}$:

The side opposite to $\sf\:60^{\circ}$ is always $\sf\:\frac{\sqrt{3}}{2}$ of the hypotenuse.