These triangles are similar Find the value of x

Mathematics

1 answer:

Grace [21]3 years ago

6 0

Answer:

C. 4

Step-by-step explanation:

This is just a common ratio. These two triangles are alike, just that one is smaller than the other. You can see that one of the sides of the big traingle is 10. The same side of the smaller triangle is 5. That means the big traingle's side is twice as big as the small circle's.

10 divided by 5= 2

If the big triangle's side got divided by 2 to get the smaller triangle's side. So, that means the other side of the big triangle, 8 is twice as big as the side on the smaller triangle, x.

8 divided by 2= x

8 divided by 2= 4, so x= 4.

This is the ratio:

8:10 to x:5

As you can see the 10 got divided by 2 to get the 5. So 8 must also get divided by 2, which equals 4.

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r-ruslan [8.4K]

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Step-by-step explanation:

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Troyanec [42]

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Tcecarenko [31]

The cosine of an angle is the x-coordinate of the point where its terminal ray intersects the unit circle. So, we can draw a line at x=-1/2 and see where it intersects the unit circle. That will tell us possible values of θ/2.

We find that vertical line intersects the unit circle at points where the rays make an angle of ±120° with the positive x-axis. If you consider only positive angles, these angles are 120° = 2π/3 radians, or 240° = 4π/3 radians. Since these are values of θ/2, the corresponding values of θ are double these values.

a) The cosine values repeat every 2π, so the general form of the smallest angle will be

... θ = 2(2π/3 + 2kπ) = 4π/3 + 4kπ

b) Similarly, the values repeat for the larger angle every 2π, so the general form of that is

... θ = 2(4π/3 + 2kπ) = 8π/3 + 4kπ

c) Using these expressions with k=0, 1, 2, we get

... θ = {4π/3, 8π/3, 16π/3, 20π/3, 28π/3, 32π/3}