 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-1/4/b/solution

A D B

is right-angled at

A

, with

A B = 2

and

A D = 1/ 2

. Another application of the Pythagorean theorem gives

D B = 2 + 1/2 = 5/2

. At the angle with vertex

D

, the adjacent side is

A D

and the hypotenuse is

D B

. Hence

cos ∠ A D B = \frac{A D}{D B} = \frac{1}{5} .

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