Activity › Discussion › Math › trigonometry
trigonometry
Posted by Geethika Pennapati on June 24, 2023 at 9:12 pmIn ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm.
Determine:
(i) sin A, cos A
(ii) sin C, cos CHarshwardhan Bhakkad replied 1 year, 1 month ago 3 Members · 2 Replies- 2 Replies
As given in question, In triangle ∆ABC. AB = 24 and BC = 7.
So the value of Hypotenuse (AC) would be 25.
Sin A = 7/25 = 0.28
Cos A = 24/25 = 0.96
Sin C = 24/25 = 0.96
Cos C = 7/25 = 0.28
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.
Log in to reply.