Use the given right triangle to find​ ratios, in reduced​ form, for sin​ A, cos​ A, and tan A.
10
26
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Part 1
Enter the ratios in reduced​ form:
sin A​ = 
  
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To find the trigonometric ratios for a right triangle, we first need to identify the lengths of the sides in relation to the angle \( A \). Given the triangle has sides of lengths 10 and 26, and one side is the hypotenuse (which is the longest side), we will assume the 26 is the hypotenuse.

Given:
- Opposite side to \( A \) (let's call it \( a \)) = 10
- Hypotenuse (\( c \)) = 26

To find the adjacent side (\( b \)), we use the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]

Plugging in the known values:
\[ 10^2 + b^2 = 26^2 \]
\[ 100 + b^2 = 676 \]
\[ b^2 = 676 - 100 \]
\[ b^2 = 576 \]
\[ b = \sqrt{576} \]
\[ b = 24 \]

Now we can find the trigonometric ratios.

### 1. \( \sin A \) (sine of angle A):
\[ \sin A = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{10}{26} \]

To reduce this fraction:
\[ \sin A = \frac{5}{13} \]

### 2. \( \cos A \) (cosine of angle A):
\[ \cos A = \frac

Learn how to find trigonometric ratios (sin, cos, tan) for angle A in a right triangle with sides 10 and 26. Includes step-by-step calculations using the Pythagorean theorem and trigonometric principles. Suitable for high school students studying trigonometry.

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