By the use of trigonometric functions, the exact value of the sine of the double of the angle ABC is equal to 24 / 25.
How to determine the exact value of a trigonometric function of a double angle
Herein we find a right triangle whose side measures are known and we need to determine the exact value of the sine of twice the angle ABC. By trigonometry, this expression is equal to:
sin 2B = 2 · sin B · cos B
Where B is an abbreviation for m ∠ ABC.
Then, by definitions of the trigonometric functions of sine and cosine and knowing that AC = 4, BC = 3 and AB = 5:
sin 2B = 2 · (4 / 5) · (3 / 5)
sin 2B = 24 / 25
The exact value of the sine of the double of the angle ABC is equal to 24 / 25.
To learn more on trigonometric functions: https://brainly.com/question/14746686
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