https://file.aiquickdraw.com/mathbot/file/1721403418391xtsd4uu6.png

I'm confused. explain very simple why are we using inverse??

Sure, let me explain it simply.

In the given problem, you need to find the angle \(\theta\) in the right triangle. You are given the lengths of the opposite side (9.3 m) and the adjacent side (4.8 m).

To find the angle \(\theta\), you can use the tangent function, which relates the opposite and adjacent sides in a right triangle:

\[ \tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{9.3}{4.8} \]

When you know the ratio of the sides and need to find the angle, you use the inverse tangent function, denoted as \(\tan^{-1}\) or \(\arctan\). This function gives you the angle whose tangent is the given ratio:

\[ \theta = \tan^{-1} \left( \frac{9.3}{4.8} \right) \]

So, by using the inverse tangent function, you can find the angle \(\theta\):

\[ \theta = \tan^{-1} \left( \frac{9.3}{4.8} \right) \approx 62.7^\circ \]

This is why we use the inverse tangent function: to find the angle when we know the tangent of the angle.

Would you like more details or have any questions?

Here are 5 questions you might want to ask:
1. How do we calculate the tangent of an angle?
2. What are other trigonometric functions and when are they used?
3. Can we find the angle using sine or cosine in this problem?
4. What is the difference between \(\tan \theta\) and \(\tan^{-1}\theta\)?
5. How can we check our answer to ensure it's correct?

**Tip:** Always make sure your calculator is in the correct mode (degrees or radians) based on the angle measurement you need.

Learn why and how we use the inverse tangent function in trigonometry to find angles in right triangles. Explore a step-by-step explanation with an example involving given opposite and adjacent sides. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation