Activity › Discussion › Math › trigonometry › Reply To: trigonometry

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To find the values of sin A, cos A, sin C, and cos C in triangle ABC, we can use the following trigonometric ratios:
• sin A = opposite side / hypotenuse = BC / AC
• cos A = adjacent side / hypotenuse = AB / AC
• sin C = opposite side / hypotenuse = AB / AC
• cos C = adjacent side / hypotenuse = BC / AC
We are given that AB = 24 cm and BC = 7 cm. We need to find AC first, which is the hypotenuse of the triangle. We
can use the Pythagorean theorem to do this:
ACA2 = ABA2 + BCA2
ACA2 = 24A2 + 7A2
ACA2 = 625
AC = 4625
AC = 25 cm
Now that we know all the side lengths of the triangle, we can find the values of the trigonometric ratios:
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•
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•
sin A
sin C
= BC/AC=7 /25
= 24 / 25 (Note: sin C is the same as sin A because angle C is the complement of angle A)
= AB/AC
Therefore, the values of sin A, cos A, sin C, and cos C are 7/25, 24/25, 24/25, and 7/25, respectively.