Diagram here: http://img172.imageshack.us/img172/1344/trig.jpg
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?
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.
01
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