Question

The angles of the triangles ABC and DEF are given as follows : A = 90${}^{\circ }$, B = 30${}^{\circ }$ D = 90${}^{\circ }$ and E = 30${}^{\circ }$. If the side BC is twice the side EF, which of the following statement is true?

• A. $\sin B=2\sin E$
• B. $\sin E=2\sin B$
• C. $\sin B=\sin E$
• D. $\sin B=2\sin A$

Answer 1

The correct option is C $\sin B=\sin E$

Given:
$\angle A={90}^{\circ }$, $\angle B={30}^{\circ }$
$\angle D={90}^{\circ }$ and $\angle E={30}^{\circ }$
Now, $\sin B=\sin 30=\frac{1}{2}$
$\sin E=\sin 30=\frac{1}{2}$
Thus, $\sin B=\sin E$