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)

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