https://file.aiquickdraw.com/mathbot/file/17263143593826m4ekcpt.jpg

The triangle in the image is a right triangle, where we know:

- Angle \( A = 35^\circ 16' \)
- The hypotenuse \( c = 964 \) meters.

We need to find:

1. Angle \( B \)
2. Side \( a \) (the side opposite angle \( A \))
3. Side \( b \) (the side adjacent to angle \( A \))

Let's solve step by step.

### 1. Find Angle \( B \)
Since the sum of angles in a triangle is \( 180^\circ \), and one of the angles is \( 90^\circ \) (right angle at \( C \)):

\[
B = 90^\circ - A
\]

Converting \( A \) into decimal form:

\[
A = 35^\circ 16' = 35 + \frac{16}{60} = 35.2667^\circ
\]

Now, subtract \( A \) from \( 90^\circ \):

\[
B = 90^\circ - 35.2667^\circ = 54.7333^\circ
\]

So, \( B \approx 54^\circ 44' \) when converted back to degrees and minutes.

### 2. Find side \( a \)
To find side \( a \), we can use the sine function:

\[
\sin(A) = \frac{a}{c}
\]

Solving for \( a \):

\[
a = c \cdot \sin(A) = 964 \cdot \sin(35.2667^\circ)
\]

Let me calculate this.The length of side \( a \) is approximately \( 557 \) meters.

### 3. Find side \( b \)
Now, we can use the cosine function to find side \( b \):

\[
\cos(A) = \frac{b}{c}
\]

Solving for \( b \):

\[
b = c \cdot \cos(A)
\]

Let me calculate that.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can manually calculate side \( b \) using the formula:

\[
b = c \cdot \cos(A)
\]

With \( A = 35.2667^\circ \) and \( c = 964 \), this will give you the value for \( b \).

Would you like more details or have any questions? Here are 5 related questions for further practice:

1. How do you convert degrees and minutes to a decimal form?
2. What is the general formula for finding angles in a triangle?
3. How can you use trigonometric identities to solve right triangles?
4. How would you find side lengths if given angles and a different side?
5. How can the tangent function help find unknown sides in a right triangle?

**Tip**: Always double-check your calculations by reapplying them to other sides or angles, ensuring consistency!

Solve the right triangle where angle A = 35° 16', hypotenuse c = 964 meters, and we need to find angle B, side a, and side b.

Solve a right triangle with a hypotenuse of 964 meters and an angle A of 35° 16'. Learn how to find the missing angle and side lengths using trigonometry. Suitable for Grades 9-12.

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