Question 869796: the area of a triangle is 8346 sqm. and two of its interior angles are 37°25' and 56°17'. What is the length of the longest side? Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! Let's call the missing angle , and the other two angles and .
The measure of the third angle is . is the largest angle.
As customary, we call the side opposite each angle (and its length) with the same letter as the opposite angle, but lowercase instead of capital: = length (in meters) of he longest side (the one opposite largest angle X), = length (in meters) of he shortest side (the one opposite smallest angle Z), and = length (in meters) of he medium-sized side (the one opposite medium-sized angle Y).
The sines of the angles rounded to 4 decimal places are:
Law of sines states that .
Substituting the values of the sines of the angles rounded to 4 decimal places: .
From those equations we can solve for and as functions of : -->
We know that the area of a triangle XYZ can be calculated from the length of two sides and the sine of the angle between them as =
and we know that = square meters
so substituting the values/expressions used/found above, meters (rounded)
