Answer:
sin(θ) = 20 / 29
Explanation:
Trigonometric ratios, or trig ratios for short, are mathematical ratios that relate the angles of a right triangle to the ratios of the lengths of its sides. These ratios are fundamental in trigonometry and are used to calculate various unknown angles or side lengths in a triangle.
The three primary trigonometric ratios are:
Sine (sin): The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse of the right triangle.
- sin(θ) = (opposite side length) / (hypotenuse length)
Cosine (cos): The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse of the right triangle.
- cos(θ) = (adjacent side length) / (hypotenuse length)
Tangent (tan): The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side of the right triangle.
- tan(θ) = (opposite side length) / (adjacent side length)
SOHCAHTOA is a mnemonic device used to remember the three primary trigonometric ratios in a right triangle: Sine, Cosine, and Tangent. It helps recall the relationships between these ratios and the sides of a right triangle.
Here's what each letter in SOHCAHTOA represents:
S = Sine
O = Opposite
H = Hypotenuse
C = Cosine
A = Adjacent
H = Hypotenuse
T = Tangent
O = Opposite
A = Adjacent
Answering the question,
We are given a right triangle. The length of the hypotenuse with respect to theta is 29, the length of the opposite side with respect to theta is 20, and the length of the adjacent side with respect to theta is 21.
Recall: sin(θ) = (opposite side length) / (hypotenuse length)
Plug in what we know to find the trig ratio:
=> sin(θ) = 20 / 29
Thus, the sine trig ratio is found.