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

Answer:

Part 1) $A=28.96^o$

Part 2) $B=46.57^o$

Part 3) $C=104.47^o$

Step-by-step 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

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

$C=180^o-75.53^o$

$C=104.47^o$