<u>Given</u>:
The given triangle is a similar triangle.
The length of the hypotenuse is 18 units.
The length of the leg is a.
The length of the part of the hypotenuse is 16 units.
We need to determine the proportion used to find the value of a.
<u>Proportion to find the value of a:</u>
We shall find the proportion to determine the value of a using the geometric mean leg rule.
Applying the leg rule, we have;
Substituting the values of hypotenuse, leg and part, we get;
Thus, the proportion used to find the value of a is
Hence, Option D is the correct answer.
The point on the y-axis is D. (0;-2)
The reciprocal of -13/7 should be -7/13
13pi/12 lies between pi and 2pi, which means sin(13pi/12) < 0
Recall the double angle identity,
sin^2(x) = (1 - cos(2x))/2
If we let x = 13pi/12, then
sin(13pi/12) = - sqrt[(1 - cos(13pi/6))/2]
where we took the negative square root because we expect a negative value.
Now, because cosine has a period of 2pi, we have
cos(13pi/6) = cos(2pi + pi/6) = cos(pi/6) = sqrt[3]/2
Then
sin(13pi/12) = - sqrt[(1 - sqrt[3]/2)/2]
sin(13pi/12) = - sqrt[2 - sqrt[3]]/2