Use the image below to answer the following question. Find the value of sin x degrees and cos y degrees. What relationship do the ratios of sin x degrees and cos y degrees share? Will give the brainliest

1) a) sin x° = 6/10

x ° = 36.87°

b) cos y° = 6/10

y° = 53.13°

2) The relationship that the ratios of sin x degrees and cos y degrees share is that:

The Opposite side in the sine function is equivalent (=) Adjacent side in the cosine function

Step-by-step explanation:

1) From the above question, we are asked to find sin x° and cos y°

Step 1

We are given 2 sides in the right angled triangle. The third side which is the Hypotenuse was not given in the diagram.

We need to find the third side which is the Hypotenuse (longest side) using Pythagoras Theorem.

This is because when solving for an angle in a right angled triangle using sine or cosine function, the Hypotenuse is required

Pythagoras Theorem =

c². = a² + b²

c = √(a² + b²)

a = 8, b = 6

c = √(8² + 6²)

c = √(64 + 36)

c = √100

c = 10

Therefore, the third side which is the Hypotenuse = 10

Step 2

Since we have found the Hypotenuse we can go ahead to solve for sin x° and cos y°

a) sin x°

The formula for the Trigonometric function of Sine is given as :

sin = Opposite/Hypotenuse

Opposite = 6

Hypotenuse = 10

sin x° = 6/10

x° = arc sin(6/10)

x ° = 36.869897646°

Approximately x° = 36.87°

b) cos y°

The formula for the Trigonometric function of Cosine is given as

cos y° = Adjacent/ Hypotenuse

Adjacent = 6

Hypotenuse = 10

cos y ° = 6/10

y ° = arc cos(6/10)

y° = 53.130102354°

Approximately , y = 53.13°

Therefore

The ratio of sin x ° = 6/10

The ratio of cos y ° = 6/10

2) The relationship that the ratios of sin x degrees and cos y degrees share is that:

The Opposite side in the sine function is equivalent (=) Adjacent side in the cosine function

h * s * a

h = history teacher

s = science teacher

a =   art teacher.

i see no data table, but just multiply the number of history teachers, science teachers, and art teachers.