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The problem is asking to solve the right triangle using the given information:

- \( a = 77.6 \, \text{yd} \)
- \( b = 42.3 \, \text{yd} \)
  
This is a right triangle, and we can use the Pythagorean theorem to find the length of the hypotenuse \( c \), and trigonometric functions to find angles \( A \) and \( B \).

### Step 1: Find \( c \) (hypotenuse)
Using the Pythagorean theorem:

\[
c = \sqrt{a^2 + b^2}
\]

### Step 2: Find angle \( A \)
To find angle \( A \), we use the tangent function:

\[
\tan(A) = \frac{b}{a}
\]

So:

\[
A = \tan^{-1}\left(\frac{b}{a}\right)
\]

### Step 3: Find angle \( B \)
Since it's a right triangle, the angles sum up to 90°:

\[
B = 90^\circ - A
\]

Now, let's calculate the values for \( c \), \( A \), and \( B \).The solutions to the right triangle are:

- \( c \) (hypotenuse) = 88.4 yards (rounded to the nearest tenth)
- \( A \) (angle opposite side \( a \)) = 28.6° (rounded to the nearest tenth)
- \( B \) (angle opposite side \( b \)) = 61.4° (rounded to the nearest tenth)

Would you like further details or have any questions?

Here are some related questions to consider:
1. How do you derive the Pythagorean theorem?
2. What is the relationship between the angles in a right triangle?
3. How can you use trigonometric functions like sine or cosine to solve a triangle?
4. What is the inverse tangent function and how is it useful in triangle problems?
5. How would this solution change if you had different side lengths?

**Tip:** Always double-check that the angles in a right triangle sum to 90°.

Solve the right triangle using the given information: a = 77.6 yd, b = 42.3 yd. Find c, angle A, and angle B.

Learn how to solve a right triangle with given sides a = 77.6 yd and b = 42.3 yd. Calculate the hypotenuse using the Pythagorean theorem and find angles A and B using trigonometric functions. Suitable for high school students (Grades 9-12).

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