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

September 30, 2021 | education

| Suppose that the AC leg is 7 cm, the BC leg is 24 cm.Follow the Pythagorean theorem, we find the length of the hypotenuse AB:

AB ^ 2 = BC ^ 2 + AC ^ 2;

AB ^ 2 = 24 ^ 2 + 7 ^ 2 = 576 + 49 = 625;

AB = √625 = 25 cm.

The large acute angle of a right-angled triangle is the angle opposite the larger leg, in this case it is the angle ∠A.

The sine of an acute angle of a right triangle is the ratio of the opposite leg to the hypotenuse:

sin A = BC / AB;

sin A = 24/25 = 0.96.

The cosine is the ratio of the adjacent leg to the hypotenuse:

cos A = AC / AB;

cos A = 7/25 = 0.28.

Tangent is the ratio of the opposite leg to the adjacent one:

tg A = BC / AC;

tg A = 24/7 = 3.43.

Answer: sin A = 0.96; cos A = 0.28; tg A = 3.43.

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