# math

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Triangle ABC has are 30cm^2, AC=9 cm and BC= 7cm. Calculate the measureof angle ACB and the larget possible length of AB.

• math -

Area = (1/2)(AC)(BC)sinØ , where Ø is angle ACB
30 =(1/2)(9)(7)sinØ
sinØ = 60/63 = .95238
Ø = 72.25° or Ø = 107.75°

The largest value of AB occurs when Ø = 107.75

by cosine law
AB^2 = 7^2 + 9^2 - 2(7)(9)cos 107.75
= 168.4187
AB = √168.4187 = 12.98

• math -

thanks :)

• math -

how did yu get 107.75?

• math -

the second angle is in quadrant II
so when you take sine-inverse, you get two answers, even though your calculator only gives you the angle in the first quadrant.

so the second angle is 180-72.25 = 107.75

• math -

pls. explain

• math -

oh yeah thaNKS.:)

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