Question

Find the value of a, b, c, and d,

type exact answers and use radicals as needed

Answer 1

Explanation:

Using trigonometrical functions we can obtain the required side lengths.

`\sin 45\degree = (a)/(16\sqrt 2)\\\\</p><p>\therefore (1)/(\sqrt 2)= (a)/(16\sqrt 2)\\\\</p><p>\therefore a = (16\sqrt 2)/(\sqrt 2)\\\\</p><p>\huge\red {\boxed {\therefore a = 16}} \\\\</p><p></p><p>\cos 45\degree = (c)/(16\sqrt 2)\\\\</p><p>\therefore (1)/(\sqrt 2)= (c)/(16\sqrt 2)\\\\</p><p>\therefore c = (16\sqrt 2)/(\sqrt 2)\\\\</p><p>\huge\purple {\boxed {\therefore c = 16}} \\\\</p><p></p><p>\sin 30\degree = (a)/(b)\\\\</p><p>\therefore (1)/(2)= (16)/(b)\\\\</p><p>\therefore b = {16*2}\\\\</p><p>\huge\orange{\boxed {\therefore b = 32}} \\\\</p><p></p><p>\tan 30\degree = (a)/(d)\\\\</p><p>\therefore (1)/(\sqrt 3)= (16)/(d)\\\\</p><p>\therefore d = {16*\sqrt 3}\\\\</p><p>\huge\pink {\boxed {\therefore d = 16\sqrt 3}} \\\\</p><p>`