Respuesta :

altavistard
1) Find the length of CB.  CB is "opposite" to angle 45 deg and is the hypotenuse of triangle BCD. 

CB = 6sqrt(2)*sin 45 deg = 6 sqrt(2) * (1 / sqrt(2) ), or:

CB = 6.

Recognize that x/6 = sin 30 deg, or x/6 = 1/2.  Thus, 2x = 6 and x = 3 (ans).
facundo3141592

Using trigonometry, we will see that x = 3

How to get the value of x?

First, we can see that the left triangle, ABC, has one of the angles equal to 45°, which means that the other non-right angle also measures 45°.

Then both its sides measure the same thing, let's say that it is L.

The hypotenuse of that triangle will be given by:

H = √(L^2 + L^2) = (√2)*L

And on the image we can see that it measures 6√2, then:

6√2 = L√2

6 = L

This means that CB = 6.

This is the hypotenuse of the right triangle BCD, and x would be the adjacent cathetus to the angle of 60°.

Then we can use the trigonometric relation:

Cos(θ) = (ajacent cathetus)/(hypotenuse).

Replacing the things we know, we get:

Cos(60°) = x/6

Cos(60°)*6 = x = 3

If you want to learn more about trigonometry, you can read:

https://brainly.com/question/6904750

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