Question

Given triangle ABC, which equation could be used to find the measure of ∠B?

right triangle ABC with AB measuring 6, AC measuring 3, and BC measuring 3 square root of 5

cos m∠B = square root of 5 over 5
sin m∠B = square root of 5 over 5
cos m∠B = square root of 5 over 2
sin m∠B = 2 square root of 5 all over 5

Answer 1

To determine the measure of ∠B in a right triangle with sides AB = 6, AC = 3, and BC = 3√5, we use the cosine function. The correct equation is cos m∠B = √5 / 5, derived from the trigonometric ratio that relates the adjacent side to the hypotenuse.

Step-by-step explanation:

To find the measure of ∠B in triangle ABC, we can use trigonometric functions that relate the sides of the triangle to its angles. Since triangle ABC is a right triangle with AB = 6, AC = 3, and BC = 3√5 (the hypotenuse), we can use the Pythagorean theorem and trigonometric ratios derived from it.

Using the given side lengths, we can determine the cosine and sine of ∠B. The cosine of an angle in a right triangle is the adjacent side divided by the hypotenuse, and the sine of an angle is the opposite side divided by the hypotenuse. Thus, for ∠B:

cos m∠B = AB / BC = 6 / (3√5) = √5 / 5

Therefore, the correct equation to find the measure of ∠B is:

cos m∠B = √5 / 5

Answer 2

Cos m∠B = √5 / 2

Sin m∠B = 1 / 2

Step-by-step explanation:

Used AI

In the given right triangle ABC, AB measures 6, AC measures 3, and BC measures 3√5.

To find the cosine and sine of angle B, we can use the ratios of the sides of the triangle.

The cosine of an angle is equal to the adjacent side divided by the hypotenuse, and the sine of an angle is equal to the opposite side divided by the hypotenuse.

Let's calculate the values:

Cos m∠B = BC / AB = (3√5) / 6 = √5 / 2

Sin m∠B = AC / AB = 3 / 6 = 1 / 2

So, the correct answers are:

Cos m∠B = √5 / 2

Sin m∠B = 1 / 2

These values represent the ratios of the sides of the triangle and give us information about the angle B in the given right triangle ABC.