https://file.aiquickdraw.com/mathbot/file/1726459065407wn8q5ve9.jpg

The image shows a right triangle where the sides \(a = 22\) and \(b = 27\), and we are asked to find the cosecant of angle \(A\).

### Step 1: Identify relevant trigonometric identities
The cosecant of an angle is the reciprocal of the sine:
\[
\csc(A) = \frac{1}{\sin(A)}
\]
For a right triangle, \(\sin(A)\) is given by:
\[
\sin(A) = \frac{\text{opposite}}{\text{hypotenuse}}
\]
where "opposite" refers to the side opposite angle \(A\), which is \(a = 22\).

### Step 2: Calculate the hypotenuse
We can use the Pythagorean theorem to find the hypotenuse \(c\):
\[
c = \sqrt{a^2 + b^2} = \sqrt{22^2 + 27^2} = \sqrt{484 + 729} = \sqrt{1213}
\]
Now, let's compute \(c\).

### Step 3: Find \(\csc(A)\)
After calculating \(c\), we will compute \(\sin(A)\) and then \(\csc(A)\).

Let me calculate that now.The hypotenuse \(c\) is approximately 34.83.

The sine of angle \(A\) is:
\[
\sin(A) \approx 0.632
\]

Thus, the cosecant of angle \(A\) is:
\[
\csc(A) \approx 1.583
\]

Let me know if you'd like further details or clarifications.

Here are five related questions to consider:
1. How would you calculate \(\cos(A)\) for this triangle?
2. What is the value of \(\tan(A)\)?
3. How does the Pythagorean identity relate to this problem?
4. What happens to \(\csc(A)\) as angle \(A\) approaches 90 degrees?
5. Can you find the other angle of the triangle using trigonometric functions?

**Tip:** Remember that cosecant is undefined for angles where the sine is zero, such as \(0^\circ\).

Use the above diagram to evaluate the following trigonometric function of angle A given a = 22 and b = 27. csc (A) = ?

Learn how to calculate the cosecant of an angle in a right triangle using the sides of the triangle and trigonometric identities. This tutorial covers finding the hypotenuse with the Pythagorean theorem and determining the sine and cosecant of an angle. Suitable for high school students in Grades 10-12.

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