Solving a triangle

Question

 

Solve for the triangle (find all angles and sides). Use different formulas.

Answer 1

You need to use the Law of Sines:

sin(A)/a = sin(B)/b = sin(C)/c

You are given one ratio,sin(A) / a = sin(50°) / 7, and part of a second ratio: sin(B) / b = sin(B) / 8. Equate this to sin(A) / a to solve for angle B:

sin(B) / 8 = sin(50) / 7

sin(B) = 8·sin(50) / 7 =

B = sin^-1(8·sin(50) / 7) = 61.1° (Use your calculator to compute the values of the sin and sin^-1)

Now you know two of the angles and two of the sides:

A = 50°

B = 61.1°

a = 7 mm

b = 8 mm

To find angle C, we know there are 180° in a triangle so angle C = 180° - 50° - 61.1° = 68.9° To find side length c, use the Law of Sines again:

sin(C) / c = sin(A )/ a

sin(68.9°) / c = sin(50°) / 7

Solve for c. Use your calculator to compute the values of the sines.

Answer 2

Let angle A=5, side a=7, side b = 8.

Need to find angles B and C and side c

We can use the sine law

sin(50)/7 = sin(B)/8

B = sin^-1((8/7)sin(50)) = 61.1°

∠C = 180 - A - B = 68.9°

sin(68.9)/c = sin(50)/7

c = 7sin(68.9)/sin(50) = 8.525 cm