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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.