https://file.aiquickdraw.com/mathbot/file/1726032377768tcu83ius.jpg

The image presents a right triangle with the following details:

- Side \( AC = 6.59 \)
- Side \( AB = 2 \)
- Angle \( \angle A = 93.48^\circ \)

We need to solve for the following:

1. Side \( b = BC \)
2. Angle \( \alpha = \angle C \)
3. Angle \( \gamma = \angle B \)

Let's start by solving the triangle step by step.

### Step 1: Use the Pythagorean Theorem to find side \( b \).

For a right triangle, we can use the Pythagorean theorem:
\[
b^2 = AC^2 + AB^2
\]
Substituting the given values:
\[
b^2 = 6.59^2 + 2^2
\]

I'll calculate this value next.The length of side \( b = BC \) is approximately \( 6.89 \).

### Step 2: Use trigonometric relationships to find the angles.

#### Finding \( \alpha = \angle C \):

We can use the tangent function:
\[
\tan(\alpha) = \frac{AB}{AC}
\]
\[
\alpha = \tan^{-1}\left(\frac{AB}{AC}\right)
\]

I'll calculate \( \alpha \) next.It seems like I can't do more advanced data analysis right now. Please try again later. However, you can calculate the remaining angles and values manually using the following steps:

### Step 2 (continued):
To find \( \alpha \), use:
\[
\alpha = \tan^{-1} \left( \frac{AB}{AC} \right) = \tan^{-1} \left( \frac{2}{6.59} \right)
\]
This will give you the angle \( \alpha \).

### Step 3: Find \( \gamma = \angle B \)
Since the sum of angles in a triangle is \( 180^\circ \), we can find \( \gamma \) by:
\[
\gamma = 180^\circ - 93.48^\circ - \alpha
\]
Substitute \( \alpha \) once it's calculated to get \( \gamma \).

Let me know if you'd like further clarifications!

### Related Questions:
1. How do you calculate angles in a triangle using trigonometric functions?
2. What is the significance of the Pythagorean theorem in solving triangles?
3. How can you apply sine, cosine, and tangent in right triangles?
4. How do you convert radians to degrees when solving angles?
5. What role does angle sum property play in solving triangles?

**Tip:** When working with right triangles, the tangent, sine, and cosine functions are extremely useful in finding unknown angles and sides!

Solve the triangle with given side lengths and angle: AB = 2, AC = 6.59, and angle A = 93.48 degrees. Find the missing side BC and angles α and γ.

Learn how to solve a right triangle where side AB = 2, side AC = 6.59, and angle A = 93.48 degrees. This problem involves using the Pythagorean Theorem, tangent functions, and angle sum properties to find side BC and angles α and γ. Suitable for students in Grades 9-12.

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