Question

In an equilateral triangle ABC , match the following ratios to the values

$$\begin{array}{cc}Trignometricratios& Values\\ \left(i\right)tan{60}^{\circ }& \left(a\right)\frac{1}{\sqrt{3}}\\ \left(ii\right)cot{30}^{\circ }& \left(b\right)\sqrt{3}\\ \left(iii\right)cosec{30}^{\circ }& \left(c\right)2\\ \left(iv\right)sec{30}^{\circ }& \left(d\right)\frac{2}{\sqrt{3}}\end{array}$$

• A. (i) –a , (ii) – b , (iii) – a , (iv) – d
• B. (i) –b , (ii) – b , (iii) – c , (iv) – d
• C. (i) –a , (ii) – b , (iii) – c , (iv) – d
• D. (i) –a , (ii) – b , (iii) – c , (iv) – b

Answer 1

The correct option is B

(i) –b , (ii) – b , (iii) – c , (iv) – d

Let each side of the equilateral triangle be a.

Length of perpendicular $AD=\frac{\sqrt{3}a}{2}$

$tan60=tanB=\frac{AD}{BD}$ = $\sqrt{3}$

$cot30=cot\frac{A}{2}$ = $\frac{AD}{BD}$ = $\sqrt{3}$

$cosec30=cosec\frac{A}{2}$ = $\frac{AB}{BD}=2$

$sec30=sec\frac{A}{2}$ = $\frac{AB}{AD}$ = $\frac{2}{\sqrt{3}}$