how do i find the opposite of a right angle triangle using cos, the adjacent and hypotenuse are 13.23 and 14.7 and the angle is 26 

To find the opposite side of a right-angled triangle using cosine, the adjacent side, the hypotenuse, and the angle, we should note that the cosine of an angle in a right triangle is defined as:

\[
\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}
\]

Given the adjacent side (\(A\)) is 13.23, the hypotenuse (\(H\)) is 14.7, and the angle (\(\theta\)) is 26°, we need to find the opposite side (\(O\)).

In a right-angled triangle, the sine of an angle is the ratio of the length of the opposite side to the hypotenuse:

\[
\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}
\]

Rearranging this formula to solve for the opposite side:

\[
\text{Opposite} = \text{Hypotenuse} \times \sin(\theta)
\]

Now we can plug in the values:

\[
\text{Opposite} = 14.7 \times \sin(26^\circ)
\]

Let's compute this.The length of the opposite side of the right-angled triangle is approximately **6.44** units.

### Summary:
- **Adjacent side** = 13.23
- **Hypotenuse** = 14.7
- **Angle** = 26°
- **Opposite side** ≈ 6.44

Would you like more details or have any other questions?

### Related Questions:
1. How do you find the adjacent side if you only know the hypotenuse and angle?
2. How do you use the Pythagorean theorem to verify the opposite side in a right triangle?
3. What is the relationship between sine and cosine for complementary angles?
4. How can you find the area of a right-angled triangle given two sides?
5. How do trigonometric functions apply to non-right triangles?

**Tip:** In trigonometry, remember that \(\sin(90^\circ - \theta) = \cos(\theta)\). This can be useful for converting between sine and cosine values.

how do i find the opposite of a right angle triangle using cos, the adjacent and hypotenuse are 13.23 and 14.7 and the angle is 26

Learn how to find the opposite side of a right-angled triangle using trigonometric functions. Given the adjacent side of 13.23, hypotenuse of 14.7, and angle of 26°, we compute the opposite side as approximately 6.44 units. Suitable for Grades 9-10.

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