Question

Use the image below to answer the following question. Find the value of sin x° and cos y°. What relationship do the ratios of sin x° and cos y° share?
A right triangle is shown with one leg measuring 12 and another leg measuring 5. The angle across from the leg measuring 5 is marked x degrees, and the angle across from the leg measuring 12 is marked y degrees.

Answer 1

The computation of the angles show that the value of sin x and cos y will be 4/5 and 3/5 respectively.

How to calculate the angles?

From the information, we've to compute the length of the hypothenuse using Pythagoras theorem.

Therefore, 4² + 3² = hypothenuse²

hypothenuse² = 16 + 9

hypothenuse² = 25

hypothenuse = ✓25.

hypothenuse = 5

Therefore, sin x = opposite/hypothenuse = 4/5

cos y = adjacent/hypothenuse = 3/5

In conclusion, the values are 4/5 and 3/5.

Learn more about angles on:

Answer 2

The values of sin x° and cos y° are $\frac{12}{13}$ and $\frac{12}{13}$. Since they are equal, the relationship between them is represented by $sin x = cos y$. This is obtained by using trigonometric ratios.

Pythagorean theorem:

This theorem states that the sum of squares of two legs of a right triangle is equal to the square of its hypotenuse. I.e.,

$a^2+b^2=h^2$

where a, and b are the two legs and 'h' is the hypotenuse of a right triangle.

Trigonometric ratios:

There are six trigonometric ratios. They are sine, cosine, tangent, secant, cosecant, and cotangent.

For a right-angle triangle,

These are ratios are calculated using the measure of an acute angle θ.

Such as

sin θ = $\frac{opposite}{hypotenuse}$

cos θ = $\frac{adjacent}{hypotenuse}$

tan θ = $\frac{opposite}{adjacent}$ and the other three are evaluated from this.

Calculating the given ratios:

Given that:

A right triangle has one leg measuring 12 and another leg measuring 5.

The angle across from the leg measuring 5 is x° and the angle across from the leg measuring 12 is y°.

So, the triangle formed is shown in the figure below.

Step 1: Calculating the measurement value of hypotenuse:

The measurement of the two legs is 12 and 5. So, the hypotenuse is calculated as,

12² + 5² = h²

⇒ 144 + 25 = h²

⇒ 169 = h²

⇒ h = 13

Therefore, the hypotenuse measures 13.

Step2: Calculating the ratios sin x° and cos y°

From the trigonometric ratios, we know that,

sin x° = $\frac{opposite}{hypotenuse}$ and

cos y°=$\frac{adjacent}{hypotenuse}$

For acute angle x°, the opposite side measures 12 and the hypotenuse is 13

So,

sin x° = $\frac{12}{13}$

Similarly, for acute angle y°, the adjacent side is 12 and the hypotenuse is 13

So,

cos y°=$\frac{12}{13}$

Thus, the two ratios are having the same value. Hence they are equal.

$sin x = cos y$.

Learn more about trigonometric ratios here:

brainly.com/question/24044139

#SPJ2