Challanging question for sine rule

[EternalSpirit]

At first the question appears to be easy but when I attempt it, I found out this question needs knowledge of where the smallest and largest angles are located in the triangle. Not stated in the Maths Quest textbook, try attempt it.

Q. Construct a suitable triangle from the following instructions and find all unknown sides and angles. One of the side is 23 cm; the smallest side is 15 cm. the smallest angle is 28 degrees.


Feel free to ask for the answers of this question as some things are not explicitly stated in the textbook.

[09Ti08]

Smallest side => smallest angle
Use sine rule:
15/sin28=23/sinx (x is the angle which is opposite 23)
So two values of x: x=46.04 or x=133.96
For x=46.04: remaining angle=105.96 => remaining side=30.72 (use sine rule again)
For x=133.96: remaining angle=18.04>smallest angle=28. This is an invalid value of x.

[EternalSpirit]

That's correct  . I also want to point out that the smallest angle is between the two longest sides of a triangle and the largest angle is between the longest and shortest side of a triangle - which is basically what you said "the angle on the opposite of the shortest side, is the smallest angle".