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

type exact answers and use radicals as needed

Find the value of a, b, c, and d, type exact answers and use radicals as needed-example-1
User Yrpalnoob
by
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1 Answer

6 votes

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>

User Mvelay
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