Solve the right triangle.
.
.
.
Question content area top right
Part 1
35 degrees 32 prime
A
B
C
a
b
966 m
Question content area bottom
Part 1
Bequals
  
54degrees 
  
28prime ​(Round to the nearest integer as​ needed.)
aequals
  
enter your response here m ​(Round to the nearest integer as​ needed.)
bequals
  
enter your response here m ​(Round to the nearest integer as​ needed.)

Let's solve the right triangle based on the given information.

Given dataLet's solve the right triangle based on the given information.

Given 
- Angle \( A = 35^\circ 32' \) 
- Angle \( B = 54^\circ 28' \) (since it’s a right triangle, the sum of angles \( A \) and \( B \) should be \( 90^\circ \)).
- Side \( c = 966 \, \text{m} \) (the hypotenuse).

We will find sides \( a \) (opposite to angle \( A \)) and \( b \) (opposite to angle \( B \)) using trigonometry.

### Step 1: Convert angles to decimal form
- \( A = 35^\circ 32' \) 
  - \( 32' \) is \( \frac{32}{60} = 0.5333^\circ \), so \( A = 35.5333^\circ \).
  
- \( B = 54^\circ 28' \)
  - \( 28' \) is \( \frac{28}{60} = 0.4667^\circ \), so \( B = 54.4667^\circ \).

### Step 2: Use sine and cosine functions

#### 1. For side \( a \) (opposite to angle \( A \)):
\[
\sin(A) = \frac{a}{c}
\]
\[
a = c \cdot \sin(A) = 966 \cdot \sin(35.5333^\circ)
\]

#### 2. For side \( b \) (opposite to angle \( B \)):
\[
\sin(B) = \frac{b}{c}
\]
\[
b = c \cdot \sin(B) = 966 \cdot \sin(54.4667^\circ)
\]

Now, let's calculate the values of \( a \) and \( b \).The values for the sides of the triangle are:
- \( a = 561 \, \text{m} \)
- \( b = 786 \, \text{m} \)

If you have further questions or need additional details, feel free to ask!

Here are some related questions to deepen understanding:
1. How do you calculate angles using inverse trigonometric functions?
2. What is the difference between degrees and radians in trigonometry?
3. How do sine and cosine relate to the sides of a right triangle?
4. What is the significance of rounding in trigonometric calculations?
5. How can the Pythagorean theorem verify the results of trigonometric calculations?

**Tip:** When solving triangles, always check if the angles add up to 180° as a quick verification step.

Solve the right triangle.

Given 
- Angle A = 35 degrees 32 prime
- Angle B = 54 degrees 28 prime (right triangle)
- Side c = 966 m (hypotenuse)

Find sides a and b.

Learn how to solve a right triangle using trigonometry with angles A = 35°32' and B = 54°28' and hypotenuse c = 966 m. This problem focuses on calculating side lengths a and b using sine functions. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation