Question

BELL RINGER: AB IS 4, BC IS 5, AC IS 7, FIND SINA, FIND COSC, FIND TANC

Answer 1

First let's draw this triangle:

Now, let's find the cosine of C using the law of cosines:

`\begin{gathered} c^2=a^2+b^2-2ab\cos (C) \\ 4^2=5^2+7^2-2\cdot5\cdot7\cdot\cos (C) \\ 16=25+49-70\cos (C) \\ 70\cos (C)=58 \\ \cos (C)=(58)/(70)=(29)/(35)=0.83 \end{gathered}`

Now, in order to find the sin(A) and tan(C), let's first find the sin(C) using the property:

`\begin{gathered} \sin ^2(C)+\cos ^2(C)=1 \\ \sin ^2(C)+((29)/(35))^2=1 \\ \sin ^2(C)=1-(841)/(1225)=(384)/(1225) \\ \sin (C)=\text{0}.56 \end{gathered}`

We can find the tan(C) using the relation:

`\begin{gathered} \tan (C)=(\sin (C))/(\cos (C)) \\ \tan (C)=(0.56)/(0.83)=0.67 \end{gathered}`

Finally, we can find sin(A) using the law of sines:

`\begin{gathered} (a)/(\sin(A))=(c)/(\sin (C)) \\ (5)/(\sin (A))=(4)/(0.56) \\ \sin (A)=0.56\cdot(5)/(4)=0.7 \end{gathered}`