Answer:
0.9063
Explanation:
Complementary angles are two angles whose sum is 90 degrees. In triangle ABC, if angle A and angle B are complementary, then we can write:
angle A + angle B = 90 degrees
Since this is a right triangle, we can use the trigonometric functions to find the lengths of the sides. The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse:
cos A = adjacent/hypotenuse
cos B = adjacent/hypotenuse
Since angles A and B are complementary, we can substitute 90 - A for B:
cos (90 - A) = adjacent/hypotenuse
sin A = adjacent/hypotenuse
So, to find the value of cos 25 degrees in this triangle, we need to find the sine of the complementary angle 65 degrees. Using the same logic as above, we can write:
sin (90 - 25) = adjacent/hypotenuse
cos 25 = adjacent/hypotenuse
We know that sin 65 = cos 25, so we can write:
cos 25 = sin 65
We can use a calculator to find that sin 65 is approximately 0.9063. Therefore, cos 25 is equivalent to approximately 0.9063.