Question

Help solving these triangles?

Triangle 1:
a= 5.5
b=4
c=3.5

Answer 1

`A=94.1^@, B=46.5^@, C=39.4^@`

Explanation:

.

We use the law of cosines:

`c^2=a^2+b^2-2abcosC`

`(3.5)^2=(5.5)^2+(4)^2-2(5.5)(4)cosC`

`12.25=30.25+16-44cosC`

`44cosC=34`

`cosC=34/44`

`C=arccos(34/44)=39.4^@`

We can either use the same law to find another angle or use the law of sines to do that. Let's use the law of sines:

`sinA/a=sinB/b=sinC/c`

`sin^2C+cos^2C=1`

`sin^2C=1-cos^2C=1-(34)^2/(44)^2=((44)^2-(34)^2)/(44)^2=780/(44)^2`

`sinC=27.93/44`

`sinB/b=sinC/c`

`sinB/4=(27.93/44)/3.5`

`sinB=(4(27.93/44))/3.5=(27.93/11)/3.5=27.93/38.5`

`B=arcsin(27.93/38.5)=46.5^@`

`A=180^@-(B+C)=180^@-(46.5^@+39.4^@)=180^@-85.9^@`

`A=94.1^@`