using the sine rule solve the following triangles DEF and find their areas

d=17cm f=22cm F=26*

could anyone please show me how to do this example so i could do the others

tha

:confused: nks

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- November 19th 2006, 04:39 AMjim49990sine rule
using the sine rule solve the following triangles DEF and find their areas

d=17cm f=22cm F=26*

could anyone please show me how to do this example so i could do the others

tha

:confused: nks - November 19th 2006, 05:10 AMtopsquark
The Law of Sines is:

So for sides d and f:

So . Now, D could merely be the reference angle, so it is possible that except that the sum of the interior angles in any triangle is 180 degrees. If D were 160.2 degrees then angle D plus angle F accounts for more than 180 degrees not even counting angle E. So angle D must be 19.8 degrees.

So we know two angles in the triangle and as I said above we know that the sum of the interior angles of a triangle is 180 degrees. So for angle E:

Employing the Law of Sines for e and f:

So side e is about 36.0 cm in length.

There are various ways to get the area of the triangle. This is Heron's formula:

where (Called the "semi-perimeter.")

So

(I am using the unrounded expression for e.)

So the area of the triangle is about .

-Dan - November 19th 2006, 06:30 AMSoroban
Hello, Jim!

Quote:

Using the Sine Rule, solve triangle and find its area.

. .

Dan did an excellent job in solving the triangle.

Here's another way to find its area.

. .

One-half the product of two sides and the sine of the included angle.

Since we know: .

. . we have: . cm².