To solve the right triangle using the given information, we can apply the Pythagorean theorem to find the hypotenuse $c$, and use trigonometric functions to find the angles $A$ and $B$.

Step 1: Find the hypotenuse $c$

The Pythagorean theorem states: $c = \sqrt{a^2 + b^2}$

Substitute $a = 78.5$ yd and $b = 40.6$ yd: $c = \sqrt{(78.5)^2 + (40.6)^2}$

Step 2: Find Angle $A$ using trigonometry

Use the tangent function: $\tan(A) = \frac{b}{a}$ To find angle $A$, we take the arctangent of both sides: $A = \tan^{-1} \left(\frac{b}{a}\right)$

Step 3: Find Angle $B$

Since it's a right triangle, the sum of angles $A$ and $B$ is 90°: $B = 90^\circ - A$

Let me calculate the values.The solution to the right triangle is as follows:

• Hypotenuse $c$ = 88.38 yards
• Angle $A$ = 27° 20' (27 degrees, 20 minutes)
• Angle $B$ = 62° 39' (62 degrees, 39 minutes)

Let me know if you need more details, or if you have any questions.

Here are 5 related questions to expand your understanding:

1. How can you verify the accuracy of the angles using trigonometric functions?
2. What is the sine, cosine, or tangent of angle $A$?
3. How does the Pythagorean theorem apply in non-right triangles?
4. How would you solve a triangle if only two angles and one side were given?
5. Can you calculate the area of this triangle using the given sides?

Tip: To convert between degrees and minutes, remember that 1 degree equals 60 minutes.