https://file.aiquickdraw.com/mathbot/file/1725560666907vu0rvita.jpg

To determine the sine of angle \( B \) in the triangle, we need to use the definition of sine for a right triangle, which is:

\[
\sin(B) = \frac{\text{opposite side to } B}{\text{hypotenuse}}
\]

From the image:

- The side opposite angle \( B \) is \( 8 \) (side \( AC \)).
- The adjacent side to angle \( B \) is \( 6 \) (side \( AB \)).
- The hypotenuse \( BC \) can be found using the Pythagorean theorem:

\[
BC^2 = AB^2 + AC^2
\]
\[
BC^2 = 6^2 + 8^2 = 36 + 64 = 100
\]
\[
BC = \sqrt{100} = 10
\]

Thus, the hypotenuse \( BC = 10 \). Now, we can calculate \( \sin(B) \):

\[
\sin(B) = \frac{AC}{BC} = \frac{8}{10} = \frac{4}{5}
\]

Therefore, the correct answer is:

\[
\boxed{4/5} \quad \text{(option c)}
\]

Would you like further details or have any other questions?

---

Here are five related questions for practice:

1. What is the cosine of angle \( B \) in the given triangle?
2. What is the tangent of angle \( B \)?
3. If the triangle were scaled up, keeping the same angles, how would the sine of angle \( B \) change?
4. Can you find the area of the triangle using the sine of angle \( B \)?
5. What is the sine of angle \( A \)?

**Tip**: Remember, sine is always the ratio of the opposite side to the hypotenuse, no matter the size of the triangle as long as the angles are fixed!

What is the sine of angle B in the triangle below?

Learn how to determine the sine of angle B in a right triangle using trigonometric ratios and the Pythagorean theorem. This problem is suitable for students in Grades 8-10 and covers key concepts of trigonometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation