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

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step-by-step explanation:

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)