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In the right triangle with sin θ =2/5, if AC= √n what is the value of n?

User Yevt
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Final answer:

In a right triangle with sin θ = 2/5, the length of the side adjacent to the angle θ is √21.

Step-by-step explanation:

In a right triangle, the sine of an angle is equal to the length of the side opposite to the angle divided by the length of the hypotenuse. So, if sin(θ) = 2/5, that means the side opposite the angle θ has a length of 2, and the hypotenuse has a length of 5. We need to find the length of the side adjacent to the angle θ.

Using the Pythagorean theorem, we have:

A2 = 52 - 22 = 25 - 4 = 21

So, the length of the side adjacent to the angle θ is √21.

Therefore, n = 21.

User Jbremnant
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