Answer:
0.17
Explanation:
41×cos(D) = 9
cos(D) = 9/41
=>
in a circle with the radius of 41 the point on the circumference of the circle for the angle D has an x-distance from the center of the circle of 9.
therefore, cos(D) = that x-distance divided by the radius (as the trigonometric functions only deliver the values for the norm circle with radius 1).
what is the y-distance (sin(D)×41) ?
r² = x² + y²
41² = 9² + y²
1681 = 81 + y²
1600 = y²
y = 40
therefore, sin(D) = 40/41
tan(D) = sin(D)/cos(D)
you know how to divide 2 fractions with each other ?
by multiplying the 2 outer factors (to top-most and bottom-most) as the top part of the result, and by multiplying the 2 inner factors for the bottom part of the result.
(40/41 - 9/41) / (40/41 / 9/41) =
= 31/41 / (40×41 / 9×41) = 9×41×31 / 40×41×41 =
= 9×31 / 40×41 = 279 / 1640 ≈ 0.17