The right triangles are given
In a part , the sides of the triangle is given 12 and 5.
In b part , all the sides are given 8,7,4.
Explanationa. To determine the hypotenuse side.
Use the Pythagoras theorem
[tex]Hypotenuse^2=Perpendicular^2+base^2[/tex]Substitute the values.
[tex]\begin{gathered} c^2=12^2+5^2 \\ c^2=144+25 \\ c=\sqrt{169} \\ c=13 \end{gathered}[/tex]b. To determine the ratios of trigonometric function from the right triangle.
Using the trigonometric ratios of sine , cosine and tan
[tex]\begin{gathered} sinC=\frac{4}{8} \\ sinC=\frac{1}{2} \end{gathered}[/tex]For cosine,
[tex]cosC=\frac{7}{8}[/tex]For tangent,
[tex]tanC=\frac{4}{7}[/tex]AnswerHence the answers are
a. The hypotenuse is c=13.
b. The trigonometric ratios are
[tex]\begin{gathered} sinC=\frac{1}{2} \\ cosC=\frac{7}{8} \\ tanC=\frac{4}{7} \end{gathered}[/tex]