Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![### Finding the Measure of Angle BAC
In this exercise, we are given a triangle and asked to determine which equation can be used to find the measure of angle BAC.
#### Diagram Description
The triangle is a right triangle with the following dimensions:
- The side AC, which is adjacent to the angle BAC, is 12 units long.
- The side AB, which is the hypotenuse of the triangle, is 13 units long.
- The side BC, which is opposite to the angle BAC, is 5 units long.
#### Problem Statement
**Question:** Which equation can be used to find the measure of angle BAC?
Below are the options provided to solve for angle BAC:
1. \(\tan^{-1}\left(\frac{5}{12}\right) = x\)
2. \(\tan^{-1}\left(\frac{12}{5}\right) = x\)
3. \(\cos^{-1}\left(\frac{12}{13}\right) = x\)
4. \(\cos^{-1}\left(\frac{13}{12}\right) = x\)
#### Analysis
To determine the correct equation for finding the measure of angle BAC, we analyze the trigonometric functions involved. For a right triangle:
- **Tangent Function (tanθ):** The ratio of the opposite side to the adjacent side.
\[
\tan(BAC) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{BC}{AC} = \frac{5}{12}
\]
- **Cosine Function (cosθ):** The ratio of the adjacent side to the hypotenuse.
\[
\cos(BAC) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{AC}{AB} = \frac{12}{13}
\]
By matching these ratios to the provided options, we can identify the correct equation used to find angle BAC.
**Correct Answer:**
The equations:
1. \(\tan^{-1}\left(\frac{5}{12}\right) = x\)
3. \(\cos^{-1}\left(\frac{12}{13}\right) = x\)
Both options can be used to find the measure of angle BAC.
It is essential for students to understand how to apply trigonometric ratios and inverse trigonometric functions to solve for angles in right triangles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fefc4e4-0fc1-4d3a-92e0-1dd9cbc9acda%2Fec181bcd-d147-42a1-a51a-0b3ec8dcf876%2F0s9mgh6.jpeg&w=3840&q=75)
Step by step
Solved in 2 steps with 1 images
