Solve the triangle if b=5 and angle B=10°.

A. a=5.0771, c=28.7939

B. a=28.7939, c = 28.3564

C. a=28.3564, c = 5.0771

D. a = 28.3564, c = 28.7939

Solving the right triangle, the correct answer is option:

D. a=28.3564, c=28.7939

Step-by-step explanation:

Hypotenuse: c

sin B = (Opposite leg to B) / Hypotenuse

sin B = b / c

Replacing the given values:

sin 10° = 5 / c

Solving for c: Cross multiplication:

c sin 10° = 5

Dividing both sides by sin 10°:

c sin 10° / sin 10° = 5 / sin 10°

c = 5 / sin 10°

c = 5 / 0.173648178

c = 28.79385236

Using the Pythagoras Theorem:

a^2+b^2=c^2

a^2+5^2=28.79385236^2

a^2+25=829.0859337

Solving for a: Subtracting 25 both sides of the equation:

a^2+25-25=829.0859337-25

a^2=804.0859337

Squart root both sides of the equation:

sqrt (a^2) = sqrt (804.0859337)

a=28.35640904

Rounding the values to four decimal places:

a=28.3564

c = 28.7939