Answer:
[tex]sin\:(J)\:=\:\frac{4\sqrt{5}}{7\sqrt{2}}[/tex]
Step-by-step explanation:
As we know that
sinФ = opposite ÷ hypotenuse
Given the triangle with
- The opposite of j is [tex]4\sqrt{5}[/tex]
The length of the hypotenuse of a right triangle can be calculated as:
[tex]c=\sqrt{a^2+b^2}[/tex]
[tex]c=\sqrt{\left(3\sqrt{2}\right)^2+\left(4\sqrt{5}\right)^2}[/tex]
[tex]c=\sqrt{3^2\cdot \:2+4^2\cdot \:5}[/tex]
[tex]c=\sqrt{18+80}[/tex]
[tex]c=\sqrt{98}[/tex]
[tex]c=\sqrt{7^2\cdot \:2}[/tex]
[tex]c=\sqrt{2}\sqrt{7^2}[/tex]
[tex]c=7\sqrt{2}[/tex]
so
sinФ = opposite ÷ hypotenuse
substituting the values Ф = J, opposite = [tex]\sqrt{5}[/tex], hypotenuse = [tex]c=7\sqrt{2}[/tex]
[tex]sin\:(J)\:=\:\frac{4\sqrt{5}}{7\sqrt{2}}[/tex]
Therefore,
[tex]sin\:(J)\:=\:\frac{4\sqrt{5}}{7\sqrt{2}}[/tex]
