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!