https://file.aiquickdraw.com/mathbot/file/1727329108244k2dx7cjx.jpg

solve triangle ABC (answer <A≈50°, <B≈73°, <C≈57°)

The given values from the image are:

\[
a = 20, \quad b = 25, \quad c = 22
\]

We need to solve the triangle, which typically involves finding all angles if the sides are known.

### To find the angles of a triangle when all sides are known, we can use the **Law of Cosines**:
\[
\cos(A) = \frac{b^2 + c^2 - a^2}{2bc}, \quad \cos(B) = \frac{a^2 + c^2 - b^2}{2ac}, \quad \cos(C) = \frac{a^2 + b^2 - c^2}{2ab}
\]

#### Step 1: Calculate angle \(A\)
\[
\cos(A) = \frac{b^2 + c^2 - a^2}{2bc} = \frac{25^2 + 22^2 - 20^2}{2 \times 25 \times 22}
\]

#### Step 2: Calculate angle \(B\)
\[
\cos(B) = \frac{a^2 + c^2 - b^2}{2ac} = \frac{20^2 + 22^2 - 25^2}{2 \times 20 \times 22}
\]

#### Step 3: Calculate angle \(C\)
\[
\cos(C) = \frac{a^2 + b^2 - c^2}{2ab} = \frac{20^2 + 25^2 - 22^2}{2 \times 20 \times 25}
\]

I will compute these values to find the approximate angles.The approximate angles of the triangle are:

\[
\angle A \approx 49.87^\circ, \quad \angle B \approx 72.88^\circ, \quad \angle C \approx 57.25^\circ
\]

These match closely with the estimated angles you provided. Would you like more details or clarifications?

Here are 5 related questions to explore:

1. How do you verify the angles of a triangle add up to \(180^\circ\)?
2. Can you explain the Law of Cosines in detail and its applications?
3. What are other methods for solving triangles besides the Law of Cosines?
4. How does the Law of Sines work for solving angles?
5. What is the relationship between side lengths and angles in any triangle?

**Tip:** When solving triangles, the Law of Cosines is particularly useful for non-right triangles where all sides are known.

Learn how to solve triangle ABC using the Law of Cosines. Given side lengths a=20, b=25, and c=22, this step-by-step solution calculates approximate angles A≈50°, B≈73°, and C≈57°. Suitable for high school students learning trigonometry and geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation