Final answer:
The cosine of ∠B is calculated by dividing the length of side BD by the length of side CB in a right triangle. Using the values given, cos(∠B) = 36/85, which results in approximately 0.4235. However, this result does not correspond to any of the offered answer choices, suggesting a possible error in the question or provided values.
Step-by-step explanation:
The student has asked how to find the cosine of ∠B in triangle BCD where ∠D is a right angle, and the lengths of the sides are given. This problem involves using trigonometric ratios in a right triangle. To find the cosine of ∠B, we will use the definition of cosine, which is the adjacent side over the hypotenuse in a right triangle. Since BD is adjacent to ∠B and CB is the hypotenuse, we have:
cos(∠B) = BD / CB
Substitute the given values:
cos(∠B) = 36 / 85
Calculating this gives us:
cos(∠B) = 0.4235
However, this value does not match any of the answer choices provided. There may have been a mistake in the question, or the values provided may be incorrect. Ensure that all sides and angles have been correctly identified and entered.