https://file.aiquickdraw.com/mathbot/file/1727846113665cgy5qzit.jpg

The image you uploaded shows a right triangle, where one angle is \( 40^\circ \), the adjacent side to this angle is 128 units, and the hypotenuse is labeled as \( x \). The task is to determine the length of the hypotenuse, \( x \).

To solve for \( x \), we can use the cosine function in trigonometry, as it relates the adjacent side and the hypotenuse in a right triangle:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

In this case:
- \( \theta = 40^\circ \)
- Adjacent side = 128
- Hypotenuse = \( x \)

Thus, the equation becomes:

\[
\cos(40^\circ) = \frac{128}{x}
\]

To solve for \( x \), rearrange the equation:

\[
x = \frac{128}{\cos(40^\circ)}
\]

Now, calculating \( \cos(40^\circ) \):

\[
\cos(40^\circ) \approx 0.7660
\]

So,

\[
x = \frac{128}{0.7660} \approx 167.17
\]

Therefore, the hypotenuse \( x \) is approximately 167.17 units.

Would you like more details, or do you have any other questions?

Here are 5 related questions for further practice:
1. How would you solve for the opposite side using the sine function?
2. What would the triangle look like if the angle was changed to 50° but the adjacent side stayed the same?
3. How can you check if your answer for the hypotenuse is reasonable?
4. What would the calculation look like if you were solving for the adjacent side instead of the hypotenuse?
5. Can you solve a triangle where all sides are given but no angles are known?

**Tip**: In right triangles, always ensure you're using the correct trigonometric function based on the sides given (adjacent, opposite, or hypotenuse).

Determine the unknown side x in the right triangle where one angle is 40°, the adjacent side is 128 units, and the unknown side is the hypotenuse.

Learn how to determine the hypotenuse of a right triangle with a 40° angle and an adjacent side of 128 units. This example uses trigonometric concepts and the cosine formula to solve for the unknown side. Suitable for Grade 10 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation