Thank you for that! Should I apply the same methods to a base plate calculation? I know I need to split the calculation or visualise the base plate split into two?

The problem I have is:

A design brief indicates three holes A,B,C to be drilled in a plate, with a=73mm, b=117mm and a =37 degrees

I need to find the possible value for the dimension of C? Should I simply split into 2 triangles and measure accordingly?

Could you post a drawing of the problem? That way you'll get a better response from everyone and I'm not always right.

I've pictured three holes A, B, C situated at three vertices. If that's the case denote the angles θ, β and γ, respectively. Now I presume when you say find the possible value of C you mean the size of the angle γ and not the hole size?

If that's the case you need to approach this problem with caution because you could enter the realm of ambiguity, where sin(β) = sin(180° - β) which means you could have two different triangles on your hands.

Do you know how to "test" for ambiguity using the sine rule?

Now if you feel most comfortable using the cosine rule, you need to find side c opposite the vertex C (I presume) and then you'll know what to do next if you take another look at the cosine rule in order to find γ.

If my interpretation of the problem is wrong, please elaborate with the aid of a diagram.

By the way, you've let a = 73mm AND a = 37°, presumably a typo?

 

Hi thanks once again, I will give the methods you suggested a try and see what I get. Can you you plesae bring me up to speed on testing for ambiguity using the sine rule?

 

Sorry for delay, please see scanned drawing of problem

 

One approach is to treat this problem as the intersection of a line with a circle of radius 73 units.

For convenience, the circle may be considered as centred at the origin with radius 73 units.

The intersecting line passes through the point [117,0] with slope of +37 degrees.

The triangle apexes are found at the points [0,0], [117,0] and either of the two intersection points.

The line intersects the circle at two distinct points. Once the coordinates of the points of intersection are known it is possible (using geometry) to determine the unknown side lengths [side 'c'] and angles [ 'B' & 'C'] for the two possible triangles.