Two Side
two sides are 400 yards and 200 yards they form an angle of 50 degrees. what is third side?someoneshowhowtodo?
A surveyor is mapping a triangular plot of land. He measures two of the sides and the angle formed by these two sides and finds that the lengths are 400 yards and 200 yards and the included angle is 50°. What is the measure of the third side of the plot of land, to the nearest yard? What is the area of this plot of land, to the nearest square yard?
please could some one show the way they did this problem. please. it would be kindly apreciated.
For the first part of the equation, you have two sides and the included angle, so you have to recognize in this case you use the law of cosines:
c^2 = a^2 + b^2 – 2ab*cos C (where C = measure of the included angle)
c^2 = (400)^2 + (200)^2 – 2*400*200*cos(50)
solving for c, we get c = 311.69 = 312 yards.
For part b, if you have two sides and an included angle in a triangle, its area is given by:
A = 1/2*a*b*sinC
A = 1/2 * 400 * 200 * sin 50
A = 30641.77 = 30642 square yards
hope that helps
Joni Mitchell – Both Sides Now (Live, 1970)
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