pick any angle (say, A) and find it via
a^2 = b^2 + c^2 - 2bc cosA
Now the area is given by 1/2 bc sinA
A triangular parcel of land has borders of lengths 55 meters, 85 meters, and 100 meters. Find the area of the parcel of land.
2 answers
checking for right-angled triangle:
is 100^2 = 55^2 + 85^2 ?
NO
so let's find the smallest angle by the cosine law:
55^2 = 100^2 + 85^2 - 2(100)(85)cosØ
cosØ = 14200/17000 = .83529..
Ø = 33.35..° , (I stored it for accuracy on my calculator
So area = (1/2)(85)(100)sin 33.35..° = appr 2336.66
or using Heron's formula
s = (1/2)(100+85+55) = 120
s-a = 120-100 = 20
s-b = 120 - 85 = 35
s-c = 120-55 = 65
area = √(120*20*35*65) = appr 2336.66
is 100^2 = 55^2 + 85^2 ?
NO
so let's find the smallest angle by the cosine law:
55^2 = 100^2 + 85^2 - 2(100)(85)cosØ
cosØ = 14200/17000 = .83529..
Ø = 33.35..° , (I stored it for accuracy on my calculator
So area = (1/2)(85)(100)sin 33.35..° = appr 2336.66
or using Heron's formula
s = (1/2)(100+85+55) = 120
s-a = 120-100 = 20
s-b = 120 - 85 = 35
s-c = 120-55 = 65
area = √(120*20*35*65) = appr 2336.66
1 answer