Tina lost 3 pounds on the first week of her diet. She gained a pound on the second week, and then lost 2 pounds a week during every week afterwards. She has been dieting for a total of 13 weeks. How many pounds has Tina lost in all?

Answer:

False, The cosine of an angle is the ratio of the opposite side over the hypotenuse.

Let ΔABC is a right angled triangle, ∠C = 90°

Figure is attached.

let ∠B be

Then the trigonometric ratios are the following:

So, clearly

Its

The only set of numbers that could be the sides of a right triangle is **(b) {2, 2, 4}**.

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Therefore, in order for a set of numbers to be the sides of a right triangle, the following equation must hold:

hypotenuse^2 = leg1^2 + leg2^2

Let's check each of the given sets:

(a) {2, 3, √13}

hypotenuse^2 = √13^2 = 13

leg1^2 = 2^2 = 4

leg2^2 = 3^2 = 9

13 ≠ 4 + 9

Therefore, {2, 3, √13} cannot be the sides of a right triangle.

(b) {2, 2, 4}

hypotenuse^2 = 4^2 = 16

leg1^2 = 2^2 = 4

leg2^2 = 2^2 = 4

16 = 4 + 4

Therefore, {2, 2, 4} can be the sides of a right triangle.

(c) {1, 2, √3}

hypotenuse^2 = √3^2 = 3

leg1^2 = 1^2 = 1

leg2^2 = 2^2 = 4

3 ≠ 1 + 4

Therefore, {1, 2, √3} cannot be the sides of a right triangle.

Therefore, the only set of numbers that could be the sides of a right triangle is **(b) {2, 2, 4}**.

Learn more about sides of a right triangle here:

brainly.com/question/33546607

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Final answer:

The set of numbers that could be the sides of a right triangle is {2,3, sqrt of 13}.

Explanation:

To determine whether a set of numbers could be the sides of a right triangle, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's check each set of numbers:

a. {2,3,√13}

b. {2,2,4}

c. (1,2,√3)

For set a, the sum of the squares of 2 and 3 is 13, which is equal to the square of √13. Therefore, set a could be the sides of a right triangle.

For set b, the sum of the squares of 2 and 2 is 8, which is not equal to the square of 4. Therefore, set b could not be the sides of a right triangle.

For set c, the sum of the squares of 1 and 2 is 5, which is not equal to the square of √3. Therefore, set c could not be the sides of a right triangle.

Therefore, the set of numbers that could be the sides of a right triangle is a. {2,3,√13}.

Learn more about right triangle here:

brainly.com/question/36869450

#SPJ12