Sine and Cosine rules question

**Colin_m** · February 3rd 2008, 08:19 AM

The diagram shows triangle ABC in which AC=4cm, BC=5cm and ACB=60 degrees.

a) Show that AB = Square root of 21

b) find the value of sin (angle ABC) in the form k(square root)7 where k is an exact fraction

Anyone know how to do this?

**bobak** · February 3rd 2008, 08:31 AM

For the first make you use the cosine rule

$AB^2 = 4^2 + 5^2 - 2 \cdot 4 \cdot 5 \cdot \cos 60$

can you finish that off ?

for the second part use the sine rule

$\frac{4}{ \sin ABC} = \frac{ \sqrt {21}}{ \sin 60}$

note $\sin 60 = \frac{ \sqrt {3} }{2}$

**Colin_m** · February 3rd 2008, 08:47 AM

yep, thanks bobak.

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