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
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.")
(I am using the unrounded expression for e.)
So the area of the triangle is about .
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.