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# Answer to Question #14838 in Trigonometry for Nathan

Question #14838
A triangular piece of land is bounded by three straight roads, two of which intersect in a right angle. The third road makes an angle of 37.6° with one of the others. The perimeter of the land is 985 yards. What is its area, to the nearest square foot?
Expert's answer
Let&#039;s denote the road triangle&#039;s sides by a, b, and c. Then we&#039;ve got the following system of equations:

a + b + c = 985;
a = c* cos(37.6);
b = c* sin(37.6);

Let&#039;s plug in last two into first to solve for c:

c*cos(37.6) + c*sin(37.6) + c = 985 ==&gt;
0.79c + 0.61c + c = 985 ==&gt;
2.4c = 985 ==&gt;
c = 410

now plug c into those initial equations for a and b to solve for a and b:

a = 326, b = 250: area = 1/2 * a*b = 0.5*326*250 = 40.750 square yards.

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