Of course, this formula can be derived, but we will leave this for you to do in the exercise (think about how the sine rule and cosine rule formulae were derived).

**Exercise** (please write answers to 3 significant figures)

**Answers**

1.) (a) 45cm^{2}, (b) 156cm^{2}, (c)52.6cm^{2} (d) 69.3cm^{2} (e) 27.6m^{2}, (f) 42.0 square miles

2.) (a) 72.3cm^{2}, (b) 28.6cm^{2}, (c) 33.1cm^{2}

3.) (a) 31.3cm^{2}, (b) 470cm^{2}, (c) 50.1mm^{2}

4.) (a) 8.51cm, (b) 6.96cm, (c) 3.97cm

5.) (a) 78.9º, (b) 31.6º, (c) 30º

**Applied questions Answers**

1.) (a) 12.7 cm^{2} (b) 82.0 cm^{2}, (c) 367 cm^{2}

2.) 26.9cm^{2}

3.) 992 m^{2}

4.) 37.1 cm^{2}

5.) 36.9 cm^{2}