Posted by **deborah** on Tuesday, March 23, 2010 at 5:13pm.

could someone please help....

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 -
**Reiny**, Tuesday, March 23, 2010 at 5:31pm
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 -
**deborah**, Tuesday, March 23, 2010 at 9:08pm
thank you very much. Reiny

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