Answer:
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
