Given tan ® = 7/24, use the Pythagorean Theorem to find the value of sin 0.

Answer 1

If your question means:

tan θ = 7 / 24, use the Pythagorean Theorem to find the value of sin θ

then:

tan θ = opposite / adjacent

Since the opposite and adjacent sides are known, use the Pythagorean theorem to find the remaining side.

hypotenuse =√ (opposite² + adjacent² )

opposite = 7

adjacent = 24

Replace the known values in the equation.

hypotenuse = √ ( 7² + 24² ) = √ ( 49 + 576 ) = √625 = 25

sine θ = opposite / hypotenuse

sin θ = 7 / 25

Answer 2

You can save yourself some calculation by learning a few of the basic Pythagorean triples, such as
3-4-5, 5-12-13, 8-15-17, 7-24-25
and their multiples.