Find the length AB.

[ttokoro]

Elementary schoole children can solve this puzzle. If you need you can use Mathcad Prime.

[AlfredFlaßhaar]

There are two intermediate solutions. In the end AB=11 in any case 😉

[terryhendicott · Accepted solution]

[ttokoro]

If we use Mathcad it is easy to find the answer. But without sqrt or functions, this puzzle becomes very hard. 

[AlfredFlaßhaar]

This task is not particularly difficult. Students should be able to solve it using the cosine law for side length and the sine formula for the area of a triangle. What is much more interesting about this problem is that solution "11" is possible in two different geometric situations.

[terryhendicott]

Hi,

Prime 9 Express version:

Cheers

Terry

[AlfredFlaßhaar]

The two solutions are AD=14.354..., BC=11.822... and AD=5.911..., BC=28.709...
They are approximations for unpleasant radicals.

[AlfredFlaßhaar]

BTW.
Numerical solutions attached. How do you solve the system symbolically? Need help.

[AlfredFlaßhaar]

Now it runs 🙂 .

[AlfredFlaßhaar]

Korrektur!

[ttokoro]

My answer is.

[AlfredFlaßhaar]

Additional task: 😉

Given pieces and requirements as usual.

But:

Instead of the given area F=60, the distance AC must now be calculated so that the area of the triangle ABC is maximum. How big is the interior angle at C?

[AlfredFlaßhaar]

Correction:
With the unusual names of the triangle vertices as shown in the sketch in the original problem, the distance AB is logically sought. I accidentally had the usual point designation in my head, where A and B limit the lower side of the triangle and C is the summit.

[Werner_E]

I would solve it that way:

Using Mathcads solving and plotting facilities it may look like this:

Mathcad 15 sheet attached