Question

A triangular lot has sides of 215m, 185m, and 125m. Find the measures of the angles at its corners

Answer 1

The measures of the angles at its corners are
`59.1\°,35.4\°,85.5\°`

Explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle A

Applying the law of cosines

`185^(2)= 215^(2)+125^(2)-2(215)(125)cos(A)`

`2(215)(125)cos(A)= 215^(2)+125^(2)-185^(2)`

`cos(A)= [215^(2)+125^(2)-185^(2)]/(2(215)(125))`
`cos(A)=0.513953`

`A=arccos(0.513953)=59.1\°`

step 2

Find the measure of angle B

Applying the law of cosines

`125^(2)= 215^(2)+185^(2)-2(215)(185)cos(B)`

`2(215)(185)cos(B)= 215^(2)+185^(2)-125^(2)`

`cos(B)= [215^(2)+185^(2)-125^(2)]/(2(215)(185))`
`cos(B)=0.81489`

`B=arccos(0.81489)=35.4\°`

step 3

Find the measure of angle C

Applying the law of cosines

`215^(2)= 125^(2)+185^(2)-2(125)(185)cos(C)`

`2(125)(185)cos(C)= 125^(2)+185^(2)-215^(2)`

`cos(C)= [125^(2)+185^(2)-215^(2)]/(2(125)(185))`
`cos(C)=0.0784`

`C=arccos(0.0784)=85.5\°`