To find the values of sine, cosine, and tangent for the given right triangle with sides a = 25 and b = 24, we can use the following trigonometric ratios:
sin(theta) = opposite/hypotenuse
cos(theta) = adjacent/hypotenuse
tan(theta) = opposite/adjacent
Given that the sides of the triangle are \(a = 25\) (opposite side) and \(b = 24\) (adjacent side), and the hypotenuse can be found using the Pythagorean theorem:
c^2 = a^2 + b^2
c^2 = 25^2 + 24^2
c^2 = 625 + 576
c^2 = 1201
c = sqrt(1201)
Now, we can find the values of sine, cosine, and tangent:
sin(theta) = opposite/hypotenuse = 25/sqrt(1201)
cos(theta) = adjacent/hypotenuse = 24/sqrt(1201)
tan(theta) = opposite/adjacent = 25/24
Therefore, the exact values of sine, cosine, and tangent for the given right triangle are:
sin = 25/sqrt(1201)
cos = 24/sqrt(1201)
tan = 25/24
