Question

(Law of Sines)

Answer 1

Answer:

Option (D) is correct.

Step-by-step explanation:

In a triangle BCD , with b, c, d as the sides of triangle.

Sine rule states when we we divide side b by the sine of angle B then it is equal to side c divided by the sine of angle C and also equal to side d divided by the sine of angle D.

Using Sine rule,

$\frac{b}{\sin B}=\frac{c}{\sin C}=\frac{d}{\sin D}$

Consider the first and third ratio,

$\frac{b}{\sin B}=\frac{d}{\sin D}$

Substitute the values of d = 3 , b= 5 and ∠D=25°

$\Rightarrow \frac{5}{\sin B}=\frac{3}{\sin 25^{\circ}}$

$\Rightarrow \sin B=\frac{\sin 25^{\circ} \times 5}{3}}$  

 $\Rightarrow \sin B=45,135$

Thus, Measure of angle B is 45 and 135 as sinB is positive is first and 2nd quadrant.

Thus, option (D) is correct.

Answer 2

The anwser is A. Hope this helps!
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