Solve the right triangle using the given information.
a equals78.5 ​yd, b equals40.6 yd find the length of c and Angle A and B in degrees and minutes

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.

Solve the right triangle using the given information. a equals 78.5 ​yd, b equals 40.6 yd find the length of c and Angle A and B in degrees and minutes.

Learn how to solve a right triangle using sides a = 78.5 yards and b = 40.6 yards. Find the hypotenuse and angles using the Pythagorean theorem and trigonometric functions. Suitable for students in Grades 9-12.

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