Question

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.

Answer 3

[AI-generated answer — Explain Bot]

To find the value of sin θ using the given information, we can follow these steps:

Step 1: Start by using the Pythagorean identity for trigonometric functions: sin²θ + cos²θ = 1.

Step 2: Since we are given the value of tan θ, which is equal to the ratio of sin θ to cos θ, we can substitute tan θ = sin θ / cos θ into the Pythagorean identity.

Step 3: Simplify the equation by multiplying both sides by cos²θ.

sin²θ + cos²θ = 1
(sin θ / cos θ)² + cos²θ = 1
sin²θ + cos²θ = cos²θ
sin²θ = cos²θ - cos²θ

Step 4: Use the trigonometric identity sin²θ + cos²θ = 1 to simplify the equation further.

sin²θ = 1 - cos²θ

Step 5: Now we can substitute the given value of tan θ = 7/24 into the equation to solve for cos θ.

tan θ = sin θ / cos θ
7/24 = sin θ / cos θ

Step 6: Since we are looking for sin θ, we need to find cos θ first. From tan θ = 7/24, we can solve for cos θ. Rearrange the equation:

cos θ = 1 / (tan θ)
cos θ = 24/7

Step 7: Substitute the value of cos θ into the equation sin²θ = 1 - cos²θ:

sin²θ = 1 - (24/7)²
sin²θ = 1 - 576/49
sin²θ = (49 - 576) / 49
sin²θ = -527 / 49

Step 8: Finally, find the value of sin θ by taking the square root of both sides:

sin θ = √(-527 / 49)

Note that the value of sin θ in this case is imaginary because the square root of a negative number is not a real number.