Question

In ABCD, the measure of angle D is 90°, BD measures 20, CB measures 29, and DC measures 21. What is the value of the cosine of angle ZC to the nearest hundredth?

A) 0.48
B) 0.68
C) 0.58
D) 0.78

Answer 1

The value of the cosine of angle C in quadrilateral ABCD is calculated by dividing the length of side DC (21) by the length of side CB (29).

Step-by-step explanation:

The question asks to find the value of the cosine of angle ZC in quadrilateral ABCD, where angle D is 90°, BD measures 20, CB measures 29, and DC measures 21. Since the question probably meant to refer to angle C instead of ZC (which does not exist in the context), we will calculate the cosine of angle C. Quadrilateral ABCD can be split into two right triangles, triangle BCD and triangle ABD. However, as we are not provided with the measurements for triangle ABD and we need the cosine of angle C, we will only focus on triangle BCD.

In a right-angled triangle, the cosine of an angle is the adjacent side divided by the hypotenuse. Since angle C is the angle in question, the adjacent side to angle C is DC, which measures 21, and the hypotenuse is CB, which measures 29. Therefore, the cosine of angle C is equal to DC/CB, which is 21/29. To find the value to the nearest hundredth, we can use a calculator to divide 21 by 29.