Solve the right triangle with Upper B equals 49.7 degrees and c equals 26.5. Round off the results according to the table below.

To solve the right triangle, given that \(\angle B = 49.7^\circ\) and \(c = 26.5\), we can determine the values of the remaining angle \(A\), side \(a\), and side \(b\).

In a right triangle, the angle sum property tells us:
\[
A + B = 90^\circ
\]
Since \(\angle B = 49.7^\circ\), we can find \(\angle A\) as:
\[
A = 90^\circ - 49.7^\circ = 40.3^\circ
\]

Next, we use trigonometric functions to find sides \(a\) and \(b\) relative to \(\angle B\):

1. **Finding \(b\):**
   Since \(c\) is the hypotenuse and \(b\) is the side adjacent to \(\angle B\), we use the cosine function:
   \[
   \cos(B) = \frac{b}{c}
   \]
   Solving for \(b\):
   \[
   b = c \cdot \cos(B) = 26.5 \cdot \cos(49.7^\circ)
   \]
   \[
   b \approx 26.5 \cdot 0.6494 \approx 17.21
   \]

2. **Finding \(a\):**
   Using the sine function, since \(a\) is opposite to \(\angle B\):
   \[
   \sin(B) = \frac{a}{c}
   \]
   Solving for \(a\):
   \[
   a = c \cdot \sin(B) = 26.5 \cdot \sin(49.7^\circ)
   \]
   \[
   a \approx 26.5 \cdot 0.7604 \approx 20.15
   \]

### Summary of Results:
- \(\angle A \approx 40.3^\circ\)
- \(a \approx 20.15\)
- \(b \approx 17.21\)
- \(c = 26.5\)

Would you like a detailed breakdown of each calculation?

Here are some related questions:
1. How can you solve a right triangle given only one side and one angle?
2. What trigonometric identities are useful in right triangle calculations?
3. How do rounding rules affect the accuracy of trigonometric solutions?
4. Why is the sum of angles in any triangle always 180 degrees?
5. How do you verify if a triangle is a right triangle using trigonometry?

**Tip:** In right triangles, remember that cosine and sine functions are complementary for angles adding up to 90 degrees, which can simplify calculations.

Solve the right triangle with B = 49.7 degrees and c = 26.5. Round off the results according to the table below.

Discover how to solve a right triangle given angle B = 49.7° and hypotenuse c = 26.5. This problem guides you through finding angle A and sides a and b using trigonometric functions. Ideal for high school students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation