Please can you explain in triangle abc angle A- 74, side a is 59.2, and side c is 60.3. Andyou have to find two possible angles for side c. The answer is 78.3 and 101.7 but where and how di you get 101.7? Thank you so very much.
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In triangle ABC
Angle A = 74 degrees
side a = 59.2
side c = 60.3
If you can find out 78.3 then the way to get the 101.7 is to do 180 - 78.3 = 101.7.
In other words, the two possible angles for angle C are supplementary, which means they add up to 180 degrees.
To construct the diagram for this with ruler and compass, which I hope they still teach somewhere, it would go like this:
1) Draw a long line with A on it. This is line b
2) At A draw another line at an angle of 74 degrees to line b. This is line c
3) Measure 60.3 along line c and put B there.
4) To find out where the line BC is, draw a circle with radius 59.2 and center B.
The circle intersects the line b in two different points. The triangle these points make with B is isosceles, so the interior angles to it are equal. One of those angles is angle C and the other one is the supplementary angle to C.
Angle A = 74 degrees
side a = 59.2
side c = 60.3
If you can find out 78.3 then the way to get the 101.7 is to do 180 - 78.3 = 101.7.
In other words, the two possible angles for angle C are supplementary, which means they add up to 180 degrees.
To construct the diagram for this with ruler and compass, which I hope they still teach somewhere, it would go like this:
1) Draw a long line with A on it. This is line b
2) At A draw another line at an angle of 74 degrees to line b. This is line c
3) Measure 60.3 along line c and put B there.
4) To find out where the line BC is, draw a circle with radius 59.2 and center B.
The circle intersects the line b in two different points. The triangle these points make with B is isosceles, so the interior angles to it are equal. One of those angles is angle C and the other one is the supplementary angle to C.