A circle with a circumference 120, degrees central angle.What is the length of the arc?
1 answer:
Answer:
Step-by-step explanation:
The complete exercise is: "A circle with circumference 18 has an arc with a 120° central angle. What is the length of the arc?"
For this exercise you need to remember the folloowing:
1. The circumference of a circle can be found with this forrmula:
Where "r" is the radius of the circle
2. The Arc length can be calculated with the following formula:
Where "r" is the radius.
In this case, you know that the circumference of this circle is 18. Then, yoy can identify that:
So, knowing that the central angle measures 120 degrees, you can substitute values into the formula for calculate the arc length and then you must evaluate.
Therefore, applying this procedure, you get the following result:
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Answer:
Step-by-step explanation:
To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.
a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:
we can substitute the value of sec(θ) in this equation:
and solve for for cos(θ)
side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by
b) since right triangle is mentioned in the question. We can use:
we know the value of cos(θ)=1\52. and by comparing the two. we can say that:
- length of the adjacent side = 1
- length of the hypotenuse = 52
we can find the third side using the Pythagoras theorem.
- length of the opposite side = √(2703) ≈ 51.9904
we can find the sin(θ) using this side:
and since