My daughter, aged 15 & in year 10, needs urgent help with this problem:
Calculate the value of.....
0.5ab sin C
a = 80mm
b = 50mm
C = 105 degrees
Thank you very much for any help that can be given.
I'd assume that the student is not allowed to use calculators for this exercise, yes?
To calculate the sine of 105 degrees, take note that the sine of an angle x between 90 to 180 degrees is equal to the sine of (180 - x).
In this case, the sine of 105 degrees is equal to the sine of (180 - 105) = sin 75degrees.
The sine of 75 degrees = sin (45 + 30 degrees).
A formula that your daughter can remember is:
Sin (A + B) = Sin A Cos B + Cos A Sin B
So... Sin 75 = Sin 45 Cos 30 + Cos 45 Sin 30
The sine of 45 degrees can be derived by cutting a square into half along its diagonal. The sine of 45 is 1/(square root of 2).
The cosine of 45 is also 1/(square root of 2).
The sine of 30 degrees can be derived by cutting an equilateral triangle into half along its height. The sine of 30 degrees is 0.5
The cosine of 30 degrees, from the same triangle, is (square root of 3)/2.
It's arithmetic from hereon.