https://file.aiquickdraw.com/mathbot/file/1726019016182md1ffjzx.jpg

The image shows a right-angled triangle with the angle of \(72^\circ\) at one vertex and a given side of 2.2 m (opposite the \(72^\circ\) angle). We are tasked with finding the length of the adjacent side, \(b\), using trigonometry.

To solve for \(b\), we can use the tangent function, which relates the angle in a right triangle to the ratio of the opposite and adjacent sides:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}
\]

Here, \(\theta = 72^\circ\), the opposite side is 2.2 m, and the adjacent side is \(b\). Rearranging the equation to solve for \(b\):

\[
b = \frac{\text{opposite}}{\tan(\theta)} = \frac{2.2}{\tan(72^\circ)}
\]

Let me calculate the value of \(b\).The length of side \(b\) is approximately \(0.715\) meters, rounded to three significant figures.

Would you like more details or have any questions about this solution?

Here are five related questions to expand on this topic:
1. How would the calculation change if the given angle was smaller, say \(60^\circ\)?
2. Can you calculate the hypotenuse of this triangle using trigonometric functions?
3. What would happen if the opposite side were doubled while keeping the angle \(72^\circ\)?
4. How do you solve for side \(a\) (the vertical side)?
5. How can you use the sine or cosine rule to verify this result?

**Tip:** Remember that the tangent function is only defined for angles between \(0^\circ\) and \(90^\circ\) and not at \(90^\circ\) itself.

In relation to the right-angle triangle, what is the value of the unknown side 'b' given the angle of 72° and the opposite side length of 2.2 meters?

Learn how to calculate the length of the adjacent side of a right-angle triangle using the tangent function. This example features a 72° angle and an opposite side length of 2.2 meters. Suitable for students in 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