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, 09:24 PMolivia59What 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 PMyeongil
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 - Jul 5th 2009, 09:31 PMolivia59wht 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 PMarze
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