Using the Pythagorean theorem, we know that:
hypotenuse^2 = adjacent side^2 + opposite side^2
- Substituting the given values, we have:
53^2 = 26^2 + opposite side^2
- Solving for the opposite side, we get:
opposite side^2 = 53^2 - 26^2
opposite side^2 = 2025
opposite side = √2025
opposite side = 45
Therefore, the length of the opposite side is 45 cm.
Verification :
The calculation is correct. You can also use the trigonometric ratio of sine to calculate the opposite side. In this case, sinθ = opposite side / hypotenuse, where θ is the angle opposite to the opposite side.
- Using the values given, sinθ = opposite side / hypotenuse = opposite side / 53. We can rearrange the formula to get:
opposite side = sinθ x hypotenuse
- To find θ, we can use the inverse sine function or arcsine. So, sinθ = opposite side / hypotenuse becomes:
θ = sin^-1 (opposite side / hypotenuse)
θ = sin^-1 (26/53)
θ = 30.96 degrees
- Substituting the values into the formula, we get:
opposite side = sinθ x hypotenuse
opposite side = sin(30.96) x 53
opposite side ≈ 45
Therefore, the length of the opposite side is approximately 45 cm, which is the same as our previous calculation.