# What is the length from B to C? What is the area of triangle?

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• Jul 5th 2009, 09:24 PM
olivia59
What is the length from B to C? What is the area of triangle?
Diagram here: http://img172.imageshack.us/img172/1344/trig.jpg

What is the length from B to C?

What is the area of triangle?
• Jul 5th 2009, 09:29 PM
yeongil
Use the Law of Cosines to find the length of BC:
\displaystyle \begin{aligned} BC^2 &= AB^2 + AC^2 - 2(AB)(AC)\cos A \\ BC^2 &= 30^2 + 12^2 - 2(30)(12)\cos 45^{\circ} \\ BC^2 &\approx 534.88 \\ BC &\approx 23.13 \end{aligned}
So the length of BC is about 23.13 m.

Then use Heron's formula to find the area. If you have a triangle with side lengths a, b & c, the formula is
$\displaystyle A = \sqrt{s(s - a)(s - b)(s - c)}$
where
$\displaystyle s = \frac{a + b + c}{2}$

In our case:
$\displaystyle s \approx \frac{30 + 12 + 23.13}{2} \approx 32.56$
and
$\displaystyle A \approx \sqrt{32.56(32.56 - 30)(32.56 - 12)(32.56 - 23.13)} \approx \sqrt{16200} \approx 127.28$

So the area of the triangle is about 127.28 sq. m.

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• Jul 5th 2009, 09:31 PM
olivia59
wht is the area
thanks. what is the area? i dont know which side is the base, i know its 1/2 x base x height
• Jul 5th 2009, 10:57 PM
arze
Quote:

Originally Posted by olivia59
thanks. what is the area? i dont know which side is the base, i know its 1/2 x base x height

there are more ways to find the area of a triangle than 1/2*base*height. there is, for example, 1/2*B*C*sinA and the like
in the answer given by yeongil, Heron's formula was used Heron's formula - Wikipedia, the free encyclopedia
hope this helps