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Part A: What is the length of diagonal AM?

Part B: What is the length of diagonal FR?

Please explain answers

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JoseyP Mar 5, 2019

#3**+2 **

OK...we got something we can work with...

If AFM is 60°.....then angle RFM = 30°

And the top left triangle is a 30-60-90 right triangle

And the side opposite the 90° angle is the side of 7

And the side opposite the 30° angle is 1/2 the side length = 1/2*7 = 3.5

So... 1/2 of diagonal MA = 1/2(7) = 3.5

So....the whole length of AM is twice this = 7 units

And angle FMR is supplemental to angle AM = 120°

Then angle AMR is 1/2 of this = 60°

And the bottom left triangle is also 30-60-90

The side opposite the 60° angle = 3.5sqrt(3) units

And this is 1/2 the length of diagonal FR

So..its length = 2 *3.5sqrt(3) = 7sqrt (3) units

CPhill Mar 5, 2019