Final answer:
To find the value of the tangent of ζB in triangle BCD, we use the formula tangent(ζB) = opposite/adjacent. The opposite side is calculated using the Pythagorean theorem and is found to be 11. Therefore, tangent(ζB) = 11/60, which to the nearest hundredth is 0.18.
Step-by-step explanation:
To find the value of the tangent of ζB (which seems to be denoted as ZB in the question) in triangle BCD to the nearest hundredth, we need to use the side lengths given: CB = 61, DC = 60, and BD = 11. Since ζB is the angle at point B, the tangent of this angle is defined by the ratio of the opposite side to the adjacent side in the right-angled triangle BCD. Therefore, we can use the following formula:
tangent(ζB) = opposite/adjacent
Given that DC is the side adjacent to ζB and CB is the hypotenuse of the right-angled triangle, the opposite side to ζB can be found using the Pythagorean theorem:
opposite = √(CB² - DC²) = √(61² - 60²) = √(3721 - 3600) = √(121) = 11
Now, we substitute the values we have to find the tangent:
tangent(ζB) = 11/60
To find the value to the nearest hundredth, we use a calculator:
tangent(ζB) ≈ 0.1833
Therefore, the value of the tangent of ζB to the nearest hundredth is approximately 0.18.