https://file.aiquickdraw.com/mathbot/file/17270499254650kp6cl32.jpg

The problem involves solving a right triangle \( \triangle ABC \), where angle \( C = 90^\circ \), side \( a = 19.2 \) cm, and the hypotenuse \( c = 45.6 \) cm. We are required to find side \( b \), using the Pythagorean theorem.

The Pythagorean theorem states:
\[
a^2 + b^2 = c^2
\]

We can rearrange this equation to solve for \( b \):
\[
b^2 = c^2 - a^2
\]
\[
b = \sqrt{c^2 - a^2}
\]

Now, let's substitute the given values:
\[
b = \sqrt{45.6^2 - 19.2^2}
\]

I will now calculate the value of \( b \).The length of side \( b \) is approximately \( 41.36 \) cm when rounded to the nearest hundredth.

Would you like more details on the steps or have any questions? Here are some related questions you might find helpful:

1. How do you solve for unknown angles in a right triangle?
2. What other methods can you use to solve right triangles?
3. How does the Pythagorean theorem apply in real-world problems?
4. Can you find the angles \( A \) and \( B \) using trigonometric ratios?
5. How do trigonometric functions like sine and cosine relate to the sides of a right triangle?

**Tip:** When solving right triangles, knowing two sides lets you calculate the third side using the Pythagorean theorem, and then you can find the angles using trigonometric ratios.

Solve the right triangle ABC, where C = 90°, a = 19.2 cm, and c = 45.6 cm. Find side b to the nearest hundredth.

Learn how to solve a right triangle ABC using the Pythagorean Theorem. Given side a = 19.2 cm and hypotenuse c = 45.6 cm, find the unknown side b rounded to the nearest hundredth. Perfect for students in Grades 8-10 studying geometry and right triangles.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation