# math

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a cottage under construction is to be 35.6m wide. the two sides of the roof are to be supported by equal rafters that meet at a 52 degree angle. determine the length of the rafters to the nearest cm using the cosine law and the sine law.

• math -

I see an isosceles triangle with equal sides of x each, the rafters, and a base of 35.6, with an angle of 52 degrees between the x's

by cosine law
35.6^2 = x^2 + x^2 - 2(x)(x)cos 52
1267.36 = 2x^2 - 2x^2(cos52)
1267.36 = x^2(2 - 2cos52)
x^2 = 1648.755
x=40.6

Using the sine law we first have to conclude that each of the base angles has to be 64 degrees
then
x/sin64 = 35.6/sin52
x = 35.6sin64/sin52 = 40.6 as before

• math -

thank you very much. Reiny

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