Question

(Law of Sines)

In △BCD, d = 3, b = 5, and m∠D = 25°. What are the possible approximate measures of angle B?

only 90°
only 155°
20° and 110°
45° and 135°

Answer 1

The anwser is A. Hope this helps!

Answer 2

Option (D) is correct.

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,

`(b)/(\sin B)=(c)/(\sin C)=(d)/(\sin D)`

Consider the first and third ratio,

`(b)/(\sin B)=(d)/(\sin D)`

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

`\Rightarrow (5)/(\sin B)=(3)/(\sin 25^(\circ))`

`\Rightarrow \sin B=(\sin 25^(\circ) * 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.