a right triangle has a hypotenuse of length 18 and an angle of 35 degrees, with a side opposite this angle of lenght 4. A second right triangle also has an angle of 35 degrees, with a hypotenuse of length 9. determine the length of the side opposite the 35 degrees angle on the second triangle
Let's assume that the side opposite the 35-degree angle in the second right triangle has a length of x.
In the first right triangle, we are given that the hypotenuse (c) has a length of 18 and the side opposite the 35-degree angle (a) has a length of 4. Using these values, we can determine the adjacent side (b) using the formula:
sin(theta) = a / c
sin(35) = 4 / 18
Now we can find cos(theta) using the formula:
cos(theta) = √(1 - sin^2(theta))
cos(35) = √(1 - (4/18)^2)
Now that we have the values of sin(theta) and cos(theta) in the first triangle, we can use them to find the length of the adjacent side (B) in the second triangle, where the hypotenuse (C) has a length of 9.
B = C * cos(theta)
B = 9 * cos(35)
Similarly, we can find the length of the side opposite the angle of 35 degrees (X) in the second triangle using the formula:
X = C * sin(theta)
X = 9 * sin(35)
Therefore, the length of the side opposite the 35-degree angle in the second triangle is 9 * sin(35).