Final answer:
The value of sin x° is 0.6 and cos y° is 0.8 for a right triangle with legs measuring 8 and 6. The sine of one acute angle is equal to the cosine of the other in a right triangle.
Step-by-step explanation:
To find the value of sin x° and cos y°, we need to apply the definitions of sine and cosine in the context of the right triangle provided. For angle x, sine is defined as the ratio of the opposite side to the hypotenuse, while cosine is defined for angle y as the ratio of the adjacent side to the hypotenuse.
We are given the lengths of the two legs of the right triangle, which are 8 and 6. However, we don't have the hypotenuse. We can find the hypotenuse (h) using the Pythagorean theorem: h = √(8² + 6²) = √(64 + 36) = √100 = 10.
Therefore, sin x° is 6/10 or 0.6, and cos y° is 8/10 or 0.8. Furthermore, since the angles x and y are complementary in a right triangle (summing up to 90 degrees), the relationship between sin x° and cos y° is that sin x° = cos y° and vice versa (sin y° = cos x°).
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
The three sides of the right triangle are:
- Hypotenuse (the longest side)
- Perpendicular (opposite side to the angle)
- Base (Adjacent side to the angle)