Answer:
Explanation:
In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse (the longest side of a right triangle, also called the hypotenuse). Therefore, to find the length of the side opposite angle θ, we can use the following formula:
opposite = sin(θ) * hypotenuse
In this case, we know that θ = 25 degrees and the adjacent side has a length of 3. Since we are dealing with a right triangle, we can use the Pythagorean theorem to find the hypotenuse:
hypotenuse = sqrt(adjacent^2 + opposite^2) = sqrt(3^2 + opposite^2) = sqrt(9 + opposite^2)
So we can substitute that value into the first equation:
opposite = sin(25) * sqrt(9 + opposite^2)
Solving for opposite, we get:
opposite = sin(25) * sqrt(9 + opposite^2)
opposite = 0.4226 * sqrt(9 + opposite^2)
We can calculate the value of sin(25) which is 0.4226.
opposite = 0.4226 * sqrt(9 + opposite^2)
opposite = 0.4226 * sqrt(opposite^2 + 9)
Square both sides of the equation to get:
opposite^2 = (0.4226 * sqrt(opposite^2 + 9))^2
opposite^2 = 0.1799 * opposite^2 + 1.5874
Subtracting 0.1799 * opposite^2 from both sides of the equation gives:
0 = 1.5874
Solving for the opposite, we get:
opposite = sqrt(1.5874)
opposite = 1.259
So the side opposite to the angle of 25 degrees is 1.259 units long, rounding to at least 3 decimal places.