Question

11. Stan Still is trying to record the dimensions of a "flag plot" (a triangular piece of land) where a house will be built. He has found that two consecutive sides of the plot have lengths of 70 yards and 95 yards. He has also determined that the angle between the two side is 82 degrees. To the nearest yard, what is the length of the final side of the plot?

Answer 1

Answer: 110 yards.

Explanation:

According to the cosine formula,

In a triangle, if a and b are two consecutive sides and x is the angle between them, then the measure of the third side (c) is given by:-

`c=√(a^2+b^2-2ab\cos x)`

As per given, a= 70 yards , b= 95 yards , x= 82 degrees

The final side =
`\sqrt{(70)^2+(95)^2-2(70)(95)\cos 82^(\circ)}`

`=√(4900+9025-13300(0.139173))\\\\=√(13925-1851) \\\\=√(12074)\\\\\approx110\text{ yards}`

I.e. the length of the final side of the plot is 110 yards.