Solve the angles and side of triangle

Question

Suppose a=3 and c=8

Find: 

b= ??

Angle A= ??

Angle B =??

Angle C= 90 degrees 

Answer 1

Greetings! Lets solve this shall we ?

We must solve this problem by using the Law of Sines such that

(sinA / a) = (sinB / b) = (sinC / c)

Since a = 3 and c = 8, we can solve for the angle A such that

(sinA / 3) = (sin90 / 8)...................Then we cross multiply such that

8sinA = 3sin90.................Then we divide 8 to both sides and notice that sin90 = 1 such that

sinA = (3/8)..............Then we take the sine inverse to both sides to solve for angle A such that

A = sin^-1(3/8) = 22^o

Since we now know angles A and C, we can calculate angle B since it is a triangle such that

Angle B = 180 - (90+22) = 180 - 112 = 68^o

Now that we have angle B, we can solve for side b such that

(sin22 / 3) = (sin68 / b)..........................We cross multiply such that

bsin22 = 3sin68......................Then divide sin22 to obtain b

b = (3sin68) / (sin22)

b = 7

I hope this helped!