Question

Use the figure below to determine the relationship between the lengths of MR and MS

Answer 1

We know that angle S of triangle MSR is 180-110, since angle S and 110 degrees are supplementary (on a line)

Using the sine rule,

MR/(sin(180-110) = MS/sin(60)

MR/sin(70)=MS/sin(60)

MR*(sqrt(3)/2)/sin(70)=MS

MS=MR(sqrt(3)/2)/sin(70)

MS=0.9216MR (to 4 decimal places)

Answer 2

Remark

I don't know if you know anything about the sine law or not. There is no obvious relationship that I see. You can find various angles and create a ratio of the two lines, but I see nothing beyond that.

Step One: Find <MSR

<MSR = 180 - 110 from the diagram.

<MSR = 70o

Step Two: Find <SMR

Every triangle has 180 degrees

<SMR + 60 + 70 = 180

<SMR + 130 = 180

<SMR = 180 - 130

<SMR = 50o

Step 3: Use the Sine Law to express the relationship between MR and MS

MR/MS = Sin(70)/Sin(60)

MR/MS = 0.9397/0.8660 = 1.0851

MR = 1.0851 * MS