Find the indicated ratios in the triangle.
Right triangle with a height of 2.56cm length of 4.65cm and hypotenuse of 5.31cm
a. tan A
b. cos C
c. sin C
How do I figure this out?
This is the most basic and rudimentary level of trigonometry.
Are you studying this ??
You probably have a right-angled triangle labeled ABC
Since you don't describe where A , B, and C are, we can't answer your question.
tan A = opposite side/ adjacent side
= .....
etc.
To solve this problem, we need to first understand the basic trigonometric functions that relate the sides of a right triangle: sine, cosine, and tangent.
1. Sine (sin): In a right triangle, the sine of an angle is defined as the length of the side opposite the angle divided by the length of the hypotenuse.
2. Cosine (cos): In a right triangle, the cosine of an angle is defined as the length of the adjacent side divided by the length of the hypotenuse.
3. Tangent (tan): In a right triangle, the tangent of an angle is defined as the length of the side opposite the angle divided by the length of the adjacent side.
Now, let's solve the problem using the given triangle dimensions:
a. tan A:
To find the tangent of angle A, we need to divide the length of the side opposite angle A by the length of the adjacent side. Looking at the triangle, we see that the side opposite angle A is the height (2.56 cm) and the adjacent side is the length (4.65 cm). Therefore, tan A = 2.56 cm / 4.65 cm.
b. cos C:
To find the cosine of angle C, we need to divide the length of the adjacent side by the length of the hypotenuse. From the triangle, we can see that the adjacent side of angle C is the length (4.65 cm) and the hypotenuse is 5.31 cm. Therefore, cos C = 4.65 cm / 5.31 cm.
c. sin C:
To find the sine of angle C, we need to divide the length of the side opposite angle C by the length of the hypotenuse. In this case, the side opposite angle C is the height (2.56 cm), and the hypotenuse is 5.31 cm. Thus, sin C = 2.56 cm / 5.31 cm.
Using these explanations and the given triangle dimensions, you can now calculate the values of the indicated ratios.