If A+B+C=180^\circ, \cot A=2 and \cot B=\frac{3}{4}, what is \sin

broggesy9

broggesy9

Answered question

2022-04-23

If A+B+C=180,cotA=2 and cotB=34, what is sinC?

Answer & Explanation

Kathleen Keller

Kathleen Keller

Beginner2022-04-24Added 20 answers

tanC=tan(A+B)=tanA+tanBtanAtanB1==112

cotC=211

cot2C=4121

csc2C=1+cot2C=125121

sin2C=121125
sinC=1155

Leia Wiggins

Leia Wiggins

Beginner2022-04-25Added 18 answers

You have
sinC=sin(180(A+B))=sin(A+B)
Then, using angle-sum formulas to obtain
cot(A+B)=cotAcotB1cotA+cotB=211
And
csc2(A+B)=cot2(A+B)+1=125121
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