Question
Type your answer If the hypotenuse has a length of 10 and the sine of an angle equals 0.3 , what is the length of the side opposite the angle?
Ask by Park Moran. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The length of the side opposite the angle is 3 units.
Solution
To find the length of the side opposite the given angle in a right triangle, you can use the definition of the sine function:
\[
\sin(\theta) = \frac{\text{Opposite Side}}{\text{Hypotenuse}}
\]
Given:
- \(\sin(\theta) = 0.3\)
- Hypotenuse = 10
Plugging in the values:
\[
0.3 = \frac{\text{Opposite Side}}{10}
\]
To find the Opposite Side:
\[
\text{Opposite Side} = 0.3 \times 10 = 3
\]
**Answer:** The length of the side opposite the angle is 3 units.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find the length of the side opposite the angle using the sine function, you can use the formula: opposite = hypotenuse * sin(angle). Given that the hypotenuse is 10 and sin(angle) = 0.3, the calculation would be: opposite = 10 * 0.3 = 3. So, the length of the side opposite the angle is 3 units. In right-angled triangles, the sine function is a convenient way to relate angles and side lengths, especially for solving problems in physics, engineering, or architecture, where knowing specific lengths is crucial for design and safety. It's like having an architectural cheat sheet to make your life easier!
