https://file.aiquickdraw.com/mathbot/file/1729514853719zzxeopo9.jpg

Determine the length of side x to the
nearest centimetre.

To determine the length of side \( x \) in the triangle shown, we can apply the **Law of Cosines**, which is useful when you know two sides and the included angle in a non-right triangle.

The formula for the Law of Cosines is:

\[
x^2 = a^2 + b^2 - 2ab \cdot \cos(C)
\]

Where:
- \( x \) is the unknown side.
- \( a = 15 \) cm, one known side.
- \( b = 18 \) cm, the other known side.
- \( C = 46^\circ \), the angle between sides \( a \) and \( b \).

Now, let's compute step by step:

\[
x^2 = 15^2 + 18^2 - 2(15)(18) \cdot \cos(46^\circ)
\]

First, calculate each part:

1. \( 15^2 = 225 \)
2. \( 18^2 = 324 \)
3. \( 2(15)(18) = 540 \)
4. \( \cos(46^\circ) \approx 0.6947 \)
5. \( 540 \cdot 0.6947 \approx 375.138 \)

Now substitute these values back into the equation:

\[
x^2 = 225 + 324 - 375.138
\]

\[
x^2 \approx 549 - 375.138
\]

\[
x^2 \approx 173.862
\]

Now take the square root:

\[
x \approx \sqrt{173.862} \approx 13.19
\]

To the nearest centimeter, the length of side \( x \) is **13 cm**.

Would you like more details or have any questions?

Here are some related questions you might explore:
1. How does the Law of Cosines compare to the Law of Sines?
2. Can the Law of Cosines be used to find angles if all sides are known?
3. What happens when the angle is obtuse in the Law of Cosines?
4. How would you solve this problem if you only knew the angle and one side?
5. Could you apply trigonometric ratios in right-angled triangles similarly?

**Tip**: Always double-check your calculator is set to degrees when solving trigonometric problems with angles in degrees.

Determine the length of side x to the nearest centimeter.

This page explains how to calculate the length of side x in a triangle using the Law of Cosines. The triangle has sides of 15 cm and 18 cm, and an included angle of 46°. Perfect 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