Trigonometry - Area of triangles

Question

A triangle has two sidesof 25cm and 30cm. The angle between the two sides is 30°.

Find:

a) the area

b) the length of it's third side 

c) the area using heron's formula

 

Answers:

a) 187.5 cm² 

b) 15.03cm

c) 187.47cm²

 

I can work out a, but not b or c :( 

Thanks in advance for your help! 

Answer 1

(b) use law of cosines

c² = a² + b² - 2(a)(b) cos30

c² = 625 + 900 - 1500((√3)/2) = 1525 - 1299 = 225.96

 

c = 15.03 cm

 

(c) Area = √(s)(s-a)(s-b)(s-c)   with s = (a+b+c)/2

 

s = (25 + 30 + 15) / 2 = 35

 

Area = √(35)(10)(5)(20) = √35000

 

Area ≈ 187