For the following right triangle, find the side length .

1 answer

To find the side length of a right triangle, we'll need some more specific information such as the lengths of the known sides or the measures of the angles.

  1. If you know the lengths of the two legs (a and b), you can use the Pythagorean theorem: \[ c = \sqrt{a^2 + b^2} \] where \( c \) is the hypotenuse.

  2. If you know one leg and the hypotenuse (let's call the leg \( a \) and the hypotenuse \( c \)): \[ b = \sqrt{c^2 - a^2} \]

  3. If you know one leg and one angle (other than the right angle), you can use trigonometric ratios. For instance, using sine or cosine: \[ \text{If } A \text{ is one of the angles:} \]

    • \( \sin(A) = \frac{\text{opposite}}{\text{hypotenuse}} \)
    • \( \cos(A) = \frac{\text{adjacent}}{\text{hypotenuse}} \)
  4. If you only have the hypotenuse and one of the other angles \( A \), you can express the sides as:

    • Opposite side = \( c \cdot \sin(A) \)
    • Adjacent side = \( c \cdot \cos(A) \)

If you provide the specific lengths or angles, I can help you calculate the unknown side length of the triangle!