Question

Find the sine of J. Write your answer in rationalized form

Answer 1

`sin\:(J)\:=\:(4√(5))/(7√(2))`

Explanation:

As we know that

sinФ = opposite ÷ hypotenuse

Given the triangle with

• Ф = J

• The opposite of j is
  `4√(5)`

The length of the hypotenuse of a right triangle can be calculated as:

`c=√(a^2+b^2)`

`c=\sqrt{\left(3√(2)\right)^2+\left(4√(5)\right)^2}`

`c=√(3^2\cdot \:2+4^2\cdot \:5)`

`c=√(18+80)`

`c=√(98)`

`c=√(7^2\cdot \:2)`

`c=√(2)√(7^2)`

`c=7√(2)`

so

sinФ = opposite ÷ hypotenuse

substituting the values Ф = J, opposite =
`√(5)`, hypotenuse =
`c=7√(2)`

`sin\:(J)\:=\:(4√(5))/(7√(2))`

Therefore,

`sin\:(J)\:=\:(4√(5))/(7√(2))`