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

**olivia59** · July 5th 2009, 09:24 PM

Diagram here: http://img172.imageshack.us/img172/1344/trig.jpg

What is the length from B to C?

What is the area of triangle?

**yeongil** · July 5th 2009, 09:29 PM

Use the Law of Cosines to find the length of BC:
$\begin{aligned} BC^2 &= AB^2 + AC^2 - 2(AB)(AC)\cos A \\ BC^2 &= 30^2 + 12^2 - 2(30)(12)\cos 45^{\circ} \\ BC^2 &\approx 534.88 \\ BC &\approx 23.13 \end{aligned}$
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
$A = \sqrt{s(s - a)(s - b)(s - c)}$
where
$s = \frac{a + b + c}{2}$

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

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

01

**olivia59** · July 5th 2009, 09:31 PM

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

**arze** · July 5th 2009, 10:57 PM

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

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