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°

In △BCD, d = 3, b = 5, and m∠D = 25°.

According to Sin law,

So, When we apply the Sin law to be △BCD

Let us plug in the value of d = 3, b = 5, and m∠D = 25°

Sin 25 degree according to the calculator is 0.44261

So, Sin 25 degree=0.443

So, we get

\frac{Sin B}{5}=\frac{0.443}{3}

So, To solve for B, let us try to get rid of 5

So, Let us multiply by 5 on both sides.

Sin B=0.7043

To solve for B, Let us take inverse of Sin on both

B=Sin^{-1}(0.70433)

B=45 degrees or B= 180 degrees -45 degrees

B=45 degrees or B=135 degrees

As, the Sin B is positive the B lies in first quadrant or second quadrant. As, sin is positive in quadrant 1 or quadrant 2 only. So, to find the angle, B in quadrant 2. we subtract the angle 45 degree from 180 degree.

So, Option D 45° and 135° Answer

step-by-step explanation:

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