Question

In an equilateral triangle ABC, find the value of sin ${30}^{\circ }$ and cos ${30}^{\circ }$

• A. 1/2,1/2
• B. 1/2, √3/2
• C. 1/√2, √2
• D. 1/√3, √3

Answer 1

The correct option is B

1/2, √3/2

Let each side of the equilateral triangle be a. A perpendicular bisector AD (which is the median and angle bisector) is drawn.

In $△$ADB

$A{D}^2$ = $A{B}^2-B{D}^2$ = $a^2-\frac{a^2}{4}$ = $\frac{3a^2}{4}$

AD = $\frac{\sqrt{3}a}{2}$

sin 30 = $\frac{BD}{AB}$ = $\frac{\left(\frac{a}{2}\right)}{a}$ = $\frac{1}{2}$

cos ${30}^{\circ }$ = $\frac{AD}{AB}$ = $\frac{\frac{\sqrt{3}a}{2}}{a}$ = $\frac{\sqrt{3}}{2}$

Using these ratios, we can determine other trigonometric ratios.