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Consider the right triangle shown below that has an interior angle measure of θ radians.

The vertical leg of the triangle is how many times as long as the hypotenuse of the triangle?
_____ times as long   

What is the value of sin(θ)?
sin(θ)=   

The horizontal leg of the triangle is how many times as long as the hypotenuse of the triangle?
 _____times as long   

What is the value of cos(θ)?
cos(θ)= 

The vertical leg of the triangle is how many times as long as the horizontal leg of the triangle?
 ______times as long   

What is the value of tan(θ)?
tan(θ)=



User Efreed
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1 Answer

3 votes

Answer:

Explanation:

To answer these questions, we need more specific information about the triangle, such as the values of the angle θ or the lengths of any of the sides. Without this information, we cannot provide specific numerical answers. However, I can give you the general relationships between the trigonometric functions and the sides of a right triangle.

In a right triangle, the hypotenuse is the side opposite the right angle, and the two legs are the other two sides.

1. The vertical leg of the triangle is never longer than the hypotenuse, so it cannot be expressed as a multiple of the hypotenuse. Therefore, we cannot determine how many times as long it is.

2. The value of sin(θ) can be determined using the trigonometric function sine, which relates the angle to the ratio of the length of the opposite side (vertical leg) to the length of the hypotenuse. So, sin(θ) = (length of vertical leg) / (length of hypotenuse).

3. Similarly, the horizontal leg of the triangle is never longer than the hypotenuse, so it cannot be expressed as a multiple of the hypotenuse. Therefore, we cannot determine how many times as long it is.

4. The value of cos(θ) can be determined using the trigonometric function cosine, which relates the angle to the ratio of the length of the adjacent side (horizontal leg) to the length of the hypotenuse. So, cos(θ) = (length of horizontal leg) / (length of hypotenuse).

5. The vertical leg and the horizontal leg are not directly related to each other in terms of their lengths. Therefore, we cannot determine how many times as long the vertical leg is compared to the horizontal leg.

6. The value of tan(θ) can be determined using the trigonometric function tangent, which relates the angle to the ratio of the length of the opposite side (vertical leg) to the length of the adjacent side (horizontal leg). So, tan(θ) = (length of vertical leg) / (length of horizontal leg).

To obtain specific answers, we need numerical values for the angle θ or the lengths of the sides in the right triangle.

User GuilhermeFGL
by
7.6k points
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