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Activity Discussion Math trigonometry Reply To: trigonometry

• ### Harshwardhan

Member
December 15, 2023 at 2:27 pm
0

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:

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.

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