Question

Which of the following values best approximates of the length of c in triangle ABC where c = 90(degrees), b = 12, and B = 15(degrees)?

c = 3.1058
c = 12.4233
c = 44.7846
c = 46.3644

In triangle ABC, find b, to the nearest degree, given a = 7, b = 10, and C is a right angle.

35(degrees)
44(degrees)
46(degrees)
55(degrees)

Solve the right triangle ABC with right angle C if B = 30(degrees) and c = 10.

a = 5, b = 5, A = 60(degrees)
a = 5, b = 8.6602, A = 60(degrees)
a = 5.7735, b = 11.5470, A = 60(degrees)
a = 8.6602, b = 5, A = 60(degrees)

Answer 1

Law of Sines states that: Sin(A)/a = Sin(B)/b= Sin(C)/C
So for the length of c: c/sin(90) = 12/sin(15) c=46.3644 units (although this answer has too many significant digits)

to find B to the nearest degree: first find length of c using pythagorus: a^2+b^2=c^2... 7^2+10^2=c^2...c=12.21 units. then law of sines... sin(90)/12.21 = sin(B)/10... sin(B)=0.817... B= sin^-1(0.817)~ 55 deg

A triangle always = 180 degrees. So angle A = 180-90-30=60 degrees. Now the law of Sines: 10/sin(90)=b/sin(30)=a/sin(60) b=5 units. a=8.66 units