Question

Solve for all the missing angles for triangle ABC: a= 10cm, b=15cm, c= 20cm. State the angles in order (Angle A,B,C) and round answers to the nearest hundredth

Answer 1

Part 1)
`A=28.96^o`

Part 2)
`B=46.57^o`

Part 3)
`C=104.47^o`

Explanation:

step 1

Find the measure of angle A

Applying the law of cosines

`a^2=b^2+c^2-2(b)(c)cos(A)`

we have

`a=10\ cm\\b=15\ cm\\c=20\ cm`

substitute

`10^2=15^2+20^2-2(15)(20)cos(A)`

Solve for A

`2(15)(20)cos(A)=15^2+20^2-10^2`

`600cos(A)=525`

`cos(A)=(525/600)`

using a calculator

`A=cos^(-1)(525/600)=28.96^o`

step 2

Find the measure of angle B

Applying the law of cosines

`b^2=a^2+c^2-2(a)(c)cos(B)`

we have

`a=10\ cm\\b=15\ cm\\c=20\ cm`

substitute

`15^2=10^2+20^2-2(10)(20)cos(B)`

Solve for A

`2(10)(20)cos(B)=10^2+20^2-15^2`

`400cos(B)=275`

`cos(B)=(275/400)`

using a calculator

`B=cos^(-1)(275/400)=46.57^o`

step 3

Find the measure of angle C

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

`A+B+C=180^o`

we have

`A=28.96^o`

`B=46.57^o`

substitute

`28.96^o+46.57^o+C=180^o`

`C=180^o-75.53^o`

`C=104.47^o`