Answer:
W= 6.745
Step By Step:
look at the first half of the triangle to find W. you were given two known angles in the triangle (56 degrees, 90 degrees) and one known side (10).
lets label all of the sides and angles first. remember, we are only looking at the first triangle as its own independent triangle. the side we are trying to find is 'w', and the side that is labeled 10 can be 'a', and the hypotenuse is 'b'. the angle at the top is W then, the 90 degree angle would be B, and the angle measuring 56 is A.
first find the measure of W. since we already have the measure of the other two angles as 56 and 90 and we know the total measure of all angles in a triangle is 180, we can easily find 180-(56+90)=34.
so you can use the Law of Sines which says if triangle ABC has sides a,b,c then
.
we are trying to find 'w' and we can use angle A and side a to do this.
we said side 'a' measured 10 degrees, and angle A was 56. angle W measured 34, like we said earlier, so set up the equation according to law of sines:
and we know these two equations equal each other:
use calculator to find sine of a 56 degree angle and 34 degree angle:
