https://file.aiquickdraw.com/mathbot/file/1728799630971qgi1v99c.jpg

The image shows a right triangle where one of the angles is \(58^\circ\), the adjacent angle is \(29^\circ\), and the horizontal leg is labeled as 430 units. We are tasked with finding the length of the vertical leg \(x\).

### To solve for \(x\), we can use trigonometric functions.

In a right triangle:
- The **tangent** of an angle is the ratio of the opposite side to the adjacent side.

For the angle \(29^\circ\), we have:
\[
\tan(29^\circ) = \frac{x}{430}
\]

Solving for \(x\):
\[
x = 430 \times \tan(29^\circ)
\]

Using a calculator to find \(\tan(29^\circ)\):
\[
x = 430 \times 0.5543 \approx 238.35
\]

Rounding to the nearest whole number:
\[
x \approx 238
\]

Thus, the length of \(x\) is approximately **238 units**.

Would you like further details or explanations on any part of this solution?

### Here are 5 related questions for further exploration:
1. What is the hypotenuse of this triangle?
2. How would the result change if the angle was slightly different, say \(30^\circ\)?
3. Can you use the cosine function to find the hypotenuse instead of the tangent?
4. How would you solve the problem if the adjacent leg was unknown but the hypotenuse was given?
5. How do you calculate the angles and sides of non-right triangles?

### Tip:
When solving right triangles, always decide which trigonometric function to use based on the known side lengths and angles—this makes solving much quicker!

Find the length x to the nearest whole number in a right triangle, where the base is 430 units, and the angles are 58° and 29°.

Learn how to find the length of the opposite side (x) in a right triangle with angles 58° and 29°, and a base of 430 units using the tangent function. This step-by-step solution is ideal for high school students (Grades 9-12) learning trigonometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation