a right triangle has a hypotenuse of length 40 and an angle of 25 degrees, with a side opposite this angle of length 16. A second right triangle also has an angle of 25 degrees, witha hypotenuse of length 10. determind the length of the side opposite the 25 degrees angle on the second triangle.
To solve this problem, we can use the sine function. The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In the first triangle, we are given the length of the hypotenuse (40) and the length of the side opposite the 25 degrees angle (16). We can use the sine function to find the length of the side adjacent to the 25 degrees angle.
sin(25 degrees) = opposite/hypotenuse
sin(25 degrees) = 16/40
sin(25 degrees) = 2/5
Now, let's use this information to find the length of the side opposite the 25 degrees angle in the second triangle.
We are given the length of the hypotenuse in the second triangle (10) and we want to find the length of the side opposite the 25 degrees angle.
sin(25 degrees) = opposite/hypotenuse
2/5 = opposite/10
Now we can solve for the length of the side opposite the 25 degrees angle in the second triangle.
opposite = (2/5) * 10
opposite = 4
Therefore, the length of the side opposite the 25 degrees angle in the second triangle is 4.