Multiple choice

$ABC$ is an isosceles right-angled triangle. Assuming $AB= BC= x$, find the value of each of the following trigonometric ratios: $\sin 45^{0}$ is $\displaystyle \dfrac{1}{\sqrt{m}}$, the value of $m$ is

  1. 1

  2. 3

  3. 2

  4. 4
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C Correct answer
Explanation

In an isosceles right triangle with sides x, x, and hypotenuse x * sqrt(2), sin(45) = opposite/hypotenuse = x / (x * sqrt(2)) = 1 / sqrt(2). Thus, m = 2.

AI explanation

Since ABC is an isosceles right-angled triangle, the perpendicular and base measure x units, making the hypotenuse x root 2 by the Pythagorean theorem. Using the trigonometric ratio for sine, sin 45 degrees equals perpendicular divided by hypotenuse, giving x divided by x root 2. Simplifying this fraction yields 1 divided by root 2, so m equals 2.

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