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2 votes
Adjacent side = 26 cm
Hypotenuse = 53 cm
Opposite side =__

2 Answers

7 votes
46.18cm would be the side
User Alex Haslam
by
8.8k points
3 votes

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.

User Eudys
by
8.4k points

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