A triangular plot of land is measured out to be exactly 1 acre, or 4,840 square yards. Two sides of the property each measure 150 yards. What is the length of the third side of the property?

Answer 1

call the angle between the congruent sides "x"

call the congruent sides "a" and "b"

use the SAS method for finding the area of a triangle (side-angle-side)

A=absin(x)/2

4840=(150)(150)sin(x)/2

9680=22,500 sin(x)

9680/22,500=sin(x)

0.436222...=sin(x)

use arcsin on your calculator

sin^-1(x)=0.4362222...

x=25.8630913°

now find the other congruent base angles

180-25.8631=154.1369

154.1369°/2=77.06845° for each base angle

now use the law of sines

call the missing side "n"

n/sin25.8631º=150/sin77.0685^º

n/0.4306=150/0.9746

0.9746n=150*0.4306

0.9746n=64.59

n=64.59/0.9746

n=66.27 yards is the length of the third side

Answer 2

The length of the third side is about 66.1625

My answer came from Herron's theorem. For a triangle of 3 sides a,b, & c the area of the triangle is

A = sqrt{s*(s-a)*(s-b)*(s-c)} where s = (a+b+c)/2

if a = 150, b = 150, & c = unknown then you solve for the unknown if A is given!

Answer 3

In order to use a formula; at least 1 angle is needed. Here's 4 formulas:

rt triangle=a^2+b^2=c^2

oblique: a^2+b^2-2ab(cosγ)=c^2

b^2+c^2-2bc(cosα)=a^2

c^2+a^2-2ac(cosβ)=b^2

Answer 4

A = (0.5)(ab)sin θ

4840 = (0.5)150² sin θ

9680 = 22500 sin θ

0.430 = sin θ

25.48° = θ

The two base angles (triangle is isosceles) are each 77.26°.

Use Law of Sines to determine length of third side.