Mathematics

Mathematics

Problem

In a right-angled triangle, sin⁡θ=35\sin\theta = \dfrac{3}{5} and the hypotenuse measures 20 cm20\,\text{cm}. Find the length of the side opposite to θ\theta. a) 10 cm10\text{ cm} b) 12 cm12\text{ cm} c) 16 cm16\text{ cm} d) 15 cm15\text{ cm}
Intuitive explanation

Since sin⁡θ\sin\theta is defined as the ratio of the opposite side to the hypotenuse, you already have the exact relationship you need—no Pythagorean theorem required. Multiply the given sine ratio by the hypotenuse length to extract the opposite side directly from the definition.

Intuitive explanation

Since sin⁡θ\sin\theta is defined as the ratio of the opposite side to the hypotenuse, you already have the exact relationship you need—no Pythagorean theorem required. Multiply the given sine ratio by the hypotenuse length to extract the opposite side directly from the definition.

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