Thread: Triangular Plot
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Old November 19th, 2008, 11:46 PM
Soroban Soroban is offline
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Hello, magentarita!

Quote:
A surveyor is mapping a triangular plot of land.
Two of the sides are 400 and 200 yards and the included angle is 50°.

(a) What is the length of the third side of the triangle, to the nearest yard?
Law of Cosines . . .

x^2 \;=\;400^2 + 200^2 - 2(400)(200)\cos50^o \;=\;97153.98245

x \;=\;311.695... \;\approx\;312 yards



Quote:
(b) What is the area of this plot of land, to the nearest square yard?
Formula: .A \;=\;\tfrac{1}{2}\;\!ab\;\!\sin C
. . The area is one-half the product of two sides and the sine of the included angle.

Therefore: .A \;=\;\tfrac{1}{2}(400)(200)\sin50^o \;=\;30641.777... \;\approx\;30,\!642 square yeards.
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