sinTheta=24/25
theta=arcsin(24/25)
Unsure how to go on from here. I'd appreciate if someone can guide me through the first few steps
Thank you
theta=arcsin(24/25)
I get 74 degrees and 106 degrees
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, we know the point P(k, 24) is 25 units away from the origin (0, 0).
So, we can set up the distance formula:
25 = sqrt((k - 0)^2 + (24 - 0)^2)
Simplifying the equation, we have:
625 = k^2 + 576
Rearranging the terms:
k^2 = 625 - 576
k^2 = 49
Taking the square root of both sides:
k = ±7
Since 0 < theta < 360, we need to consider the positive value of k, which is k = 7.
Now, we know the x-coordinate of the point P is 7, and the y-coordinate is 24. To find the angle theta, we can use inverse trigonometric functions.
We have:
tan(theta) = y/x
tan(theta) = 24/7
Now, we need to find the angle whose tangent is 24/7. We can use the inverse tangent function (also known as arctan or tan^(-1)).
theta = arctan(24/7)
Using a calculator or a trigonometric table, we can find the approximate value of theta:
theta ≈ 74.38 degrees
Therefore, the measure of theta is approximately 74.38 degrees.