Question

What is the cosine ration ? HELP PLZ !!

Answer 1

The cosine ratio for this question is 3/5. By simple formula  

Cos(theta) = Base / Hypotenuse

Further Explanation:

In this example we has a right triangle, it has base named as XY, altitude as YZ and hypotenuse as XZ because XZ is in front of 90 degree.

Calculation:

We can simpley find out the cosine ration by simple method.

Data:

XY=? ,  YZ = 6 , XZ = 7.5

Solution:

We have to find the cosine ratio so the formula for cosine ratio is

Cos(theta) = Base / Hypotenuse.

Cos (Theta) = XY / XZ        

Here XY is Base and XZ as Hypotenuse.

By putting the values:

Cos(Theta) = XY / 7.5 --------------(i)

Here we can get the value of XY by phethagoras theorem.  

XZ2 = XY2  +  YZ2  

By putting the value if XZ and YZ respectively.

(7.5)2 = XY2 +  (6)2  

XY2 = (7.5)2 – (6)2

Taking square root on both sides

XY = 4.5

Put the values of XY in euation no (i)

Cos(Theta) = 4.5 / 7.5

Multiply by 2 on up and down

Cos(theta) = 9 / 15

Cos (Theta) = 3 / 5.

Answer Details:

Subject: mathematics

Level: Middle School

Key Words:

Calculation:

Data:

Solution:

For further Evaluation:

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Answer 2

The cosine of angle X is

$\cos X=\dfrac{XY}{XZ}=\dfrac{XY}{7.5}$

By the Pythagorean theorem, we have

$XY^2+YZ^2=XZ^2\implies XY=\sqrt{7.5^2-6^2}=4.5$

Then

$\cos X=\dfrac{XY}{XZ}=\dfrac{4.5}{7.5}$

Multiplying numerator and denominator by 2, we get $\dfrac9{15}$.