9514 1404 393
Answer:
76.5 units
Explanation:
This is an interesting question. The side lengths are proportional to the sine of the opposite angle. So, we can find a scale factor for the given length by adding the sines of the angles and dividing by the sine of the angle opposite the given side.
The three angles are ...
43°, 63° and 74° (the supplement of the sum of the other two)
So, the scale factor mentioned above is ...
(sin(43°) +sin(63°) +sin(74°))/sin(74°) ≈ 2.636396
Then the perimeter of the triangle is ...
(2.636396)(29) ≈ 76.5 . . . units