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An acute angle, θ, is in a right triangle such that sin of theta is equal to 3 over 8 period What is the value of cot θ?

square root of 55 over 3
the quantity 3 times the square root of 55 end quantity over 55
square root of 55 over 8
the quantity 8 times the square root of 55 end quantity over 5

Respuesta :

facundo3141592

We want to find the value of cot(θ) given that sin(θ) = 3/8 and θ is an angle in a right triangle, we will get:

cot(θ) = (√55)/3

So we know that θ is an acute angle in a right triangle, and we get:

sin(θ) = 3/8

Remember that:

  • sin(θ) = (opposite cathetus)/(hypotenuse)
  • hypotenuse = √(  (opposite cathetus)^2 +  (adjacent cathetus)^2)

Then we have:

opposite cathetus = 3

hypotenuse = 8 = √(3^2 +  (adjacent cathetus)^2)

Now we can solve this for the adjacent cathetus, so we get:

adjacent cathetus = √(8^2 - 3^2) = √55

And we know that:

cot(θ) = (adjacent cathetus)/(opposite cathetus)

Then we get:

cot(θ) = (√55)/3

If you want to learn more, you can read:

https://brainly.com/question/15345177

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