https://file.aiquickdraw.com/mathbot/file/17264444778357hsx3rej.jpg

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The triangle problem presents a right triangle where:
- \( a = 78.7 \, \text{yd} \) (adjacent side),
- \( b = 40.9 \, \text{yd} \) (opposite side).

We need to:
1. Find the hypotenuse \( c \) using the Pythagorean theorem.
2. Determine angles \( A \) and \( B \) using trigonometric functions.

### Step 1: Hypotenuse \( c \)
The Pythagorean theorem states:
\[
c = \sqrt{a^2 + b^2}
\]

### Step 2: Angle \( A \)
Using the tangent function:
\[
\tan(A) = \frac{b}{a}, \quad A = \tan^{-1}\left(\frac{b}{a}\right)
\]

### Step 3: Angle \( B \)
Angle \( B \) can be found since it's the complement of angle \( A \) in a right triangle:
\[
B = 90^\circ - A
\]

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Here are some related questions you might be interested in:
1. How can I find the area of a right triangle given two sides?
2. What is the sine, cosine, and tangent of the angles in this triangle?
3. How do I calculate the perimeter of the triangle?
4. How does the law of sines work in a non-right triangle?
5. How would this problem change if the triangle were not a right triangle?

**Tip:** Always double-check that you are using the correct units and rounding appropriately when solving trigonometric problems.

Solve the right triangle using the given information: a = 78.7 yd, b = 40.9 yd. Find the hypotenuse c and angles A and B.

Learn how to solve a right triangle with sides a = 78.7 yd and b = 40.9 yd. This problem involves using the Pythagorean theorem to find the hypotenuse and trigonometric functions to calculate the angles. Ideal for students in Grades 9-12.

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