# Find the sine, cosine, tangent of the larger acute angle of a right-angled triangle with legs 7 cm and 24 cm.

July 28, 2021 | education

| 1) In the condition of the problem it is said that we need a larger angle, and this one lies against the larger side. 24> 7, which means that the leg of 24 cm lies opposite the larger acute angle. 2) We are looking for the hypotenuse of the triangle, according to the Pythagorean theorem. The square of the hypotenuse is equal to the sum of the squares of the legs. BC = √ (24 ^ 2 + 7 ^ 2) = √625 = 25 3) The sine of an angle is the ratio of the opposite leg to the hypotenuse. Hence sinx = 24/25. 4) The cosine of the angle is the ratio of the leg adjacent to the hypotenuse. Hence cosx = 7/25. 5) Tangent is the ratio of sine to cosine: tgx = 24/7 = 3 3/7.

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