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Construct a triangle ABC if perimeter is 11.5 base angle is angle B=60°and angle C=50°.
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1. Although it was not declared explicitly in the condition, it is assumed implicitly
that the angles B and C are given as the instances at the plane.
It doesn't matter that they are 60° and 50°. I mean: their numerical values do not matter.
What really does matter is that these angles are given as instances, so you do not need worry on construction the angle of 50°.
(So, actually the condition in this post is not precisely correct.
The correct formulation should be like this:
"Construct a triangle ABC with the given perimeter and two given angles B and C.")
How it is really formulated in the post is making a fog . . .
2. Having given these two angles B and C, construct an arbitrary triangle with these two angles B and C.
I mean, construct a triangle with an arbitrary side length concluded between these two angles.
It is obvious how to do it, and since it is obvious, I will not explain it more.
3. Now, the triangle you constructed is similar to the required triangle.
All you need to do is to adjust the triangle you just constructed, in a way to get
the perimeter of the adjusted triangle 11.5 cm (11.5 units . . . ).
It is clear that the major task is to adjust the side BC of the constructed triangle.
4. The key procedure for it is described in the lesson
HOW TO construct the segment whose length is an unknown term of a proportion
in this site.
5. On one side of the given angle B mark the segment whose length is the perimeter of the constructed triangle.
Mark its endpoint as P.
On the same side of the given angle attach the segment whose length is the corresponding side BC of the constructed triangle.
Mark the endpoint as Q.
On the other side of the given angle B mark the segment whose length is the GIVEN perimeter.
Mark its endpoint as R.
Connect P and R.
Next draw a straight line from Q parallel to PR.
Mark S its intersection with BR.
Now RS is the actual side "newBC" of your adjusted triangle.
6. Re-construct the triangle with the side "newBC" and the angles B and C.
7. The problem is solved.
