https://file.aiquickdraw.com/mathbot/file/1727218582357cmjj4zzk.jpg

We are given a right-angled triangle with one of the non-right angles labeled as \( x \), the adjacent side as 27.2 mm, and the opposite side as 15.8 mm.

### Steps to solve for angle \( x \):

1. **Use the cosine formula:**
   \[
   \cos(x) = \frac{\text{adjacent}}{\text{hypotenuse}}
   \]
   However, the hypotenuse is not provided, so we should first calculate it using the Pythagorean theorem.

2. **Find the hypotenuse:**
   Using the Pythagorean theorem:
   \[
   \text{hypotenuse}^2 = (\text{adjacent side})^2 + (\text{opposite side})^2
   \]
   \[
   \text{hypotenuse}^2 = (27.2)^2 + (15.8)^2
   \]
   \[
   \text{hypotenuse} = \sqrt{27.2^2 + 15.8^2}
   \]

3. **Calculate \( \cos(x) \):**
   After finding the hypotenuse, we can use the cosine function to find the value of \( x \):
   \[
   \cos(x) = \frac{27.2}{\text{hypotenuse}}
   \]
   Solve for \( x \) by taking the inverse cosine:
   \[
   x = \cos^{-1} \left( \frac{27.2}{\text{hypotenuse}} \right)
   \]

Let's compute the values.The hypotenuse of the triangle is approximately 31.46 mm, and the angle \( x \) is approximately \( 30.2^\circ \) to 1 decimal place.

Would you like further details on the steps or explanations?

Here are five related questions to deepen your understanding:
1. How can you use sine or tangent to solve for angle \( x \)?
2. How would the calculation change if the triangle had different side lengths?
3. What is the relationship between cosine, sine, and tangent in trigonometry?
4. Can you derive other angles in the triangle using basic trigonometric identities?
5. How would you find the area of this triangle?

**Tip:** The Pythagorean theorem is crucial for solving right-angled triangles when you're missing the hypotenuse or other sides.

By first finding cos(x), work out the size of angle x. The triangle has an adjacent side of 27.2 mm and an opposite side of 15.8 mm. Give your answer in degrees to 1 decimal place.

Learn how to solve for angle x in a right-angled triangle using trigonometry. Given an adjacent side of 27.2 mm and an opposite side of 15.8 mm, follow step-by-step instructions to use the cosine function and the Pythagorean theorem. Suitable for Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation