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°.