A right triangle has a hypotenuse of length 40 and an angle of 25°, with a side opposite this angle of length 16. A second right triangle also has an angle of 25°, with a hypotenuse of length 10. Determine the length of the side opposite the 25° angle on the second triangle.(1 point)
The side opposite the second triangle’s 25° angle has length 4.
The side opposite the second triangle’s 25° angle has length 64.
The side opposite the second triangle’s 25°angle has length 8√21
The side opposite the second triangle’s 25° angle has length 8.
To find the length of the side opposite the 25° angle in the second triangle, we can use the fact that in a right triangle, the lengths of the sides are proportional to the lengths of the other sides opposite the corresponding angles.
In the first triangle, we can use the sine function to find the length of the side opposite the 25° angle. The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. So, we have:
sin(25°) = 16/40
solving for the length of the side opposite the 25° angle, we have:
16/40 = x/10
cross-multiplying, we get:
10(16) = 40x
dividing both sides by 40, we get:
x = 160/40
x = 4
So, the length of the side opposite the 25° angle in the second triangle is 4. Hence, the correct answer is:
The side opposite the second triangle’s 25° angle has length 4.