https://file.aiquickdraw.com/mathbot/file/1729091457434t6k6xo0y.jpg

In this problem, we are given a right triangle with one angle \(50^\circ\), and the side opposite the right angle (\(AB\)) labeled as \(18\). We are asked to solve for side \(b\) (the base) and side \(c\) (the hypotenuse) of the triangle, and the other angle, \(B = 40^\circ\), has been provided in the box. We'll use trigonometric functions to solve this.

### Step 1: Use Trigonometric Ratios
- We know angle \(A = 50^\circ\) and side \(AB = 18\). 

#### 1. Solving for side \(c\) (the hypotenuse):
We can use the sine function because:
\[
\sin(A) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{18}{c}
\]
So,
\[
c = \frac{18}{\sin(50^\circ)}
\]
\[
c \approx \frac{18}{0.7660} \approx 23.5
\]
Thus, \(c \approx 23.5\).

#### 2. Solving for side \(b\) (the base):
We can use the tangent function because:
\[
\tan(A) = \frac{\text{opposite}}{\text{adjacent}} = \frac{18}{b}
\]
So,
\[
b = \frac{18}{\tan(50^\circ)}
\]
\[
b \approx \frac{18}{1.1918} \approx 15.1
\]
Thus, \(b \approx 15.1\).

### Final Results:
- \(b \approx 15.1\)
- \(c \approx 23.5\)

Would you like more details or have any questions on this? 

Here are 5 related questions:
1. How do you use the cosine function to verify the base \(b\)?
2. What happens if you round the values to different decimal places?
3. How can you find angle \(B\) if it wasn't given?
4. How does the Pythagorean theorem apply to this triangle?
5. Can you solve this triangle if a different side is given?

**Tip:** Always double-check if your calculator is in degrees mode when working with angles in degrees!

Solve the right triangle with angle A = 50°, side opposite to A = 18, and angle B = 40°.

Learn how to solve a right triangle where one angle is 50°, the opposite side is 18, and the other angle is 40°. This problem uses trigonometric functions, such as sine and tangent, to find the base and hypotenuse. Suitable for high school 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