Find the missing side lengths. Leave the answers as radicals in the simplest form. A) a=(7√(6) )/(2) , b=(7√(3) )/(3) \\\\B) a=7√(2) , b=(7√(3) )/(3) \\\\C) a=(7√(6) )/(2), b=7\…

Question

Find the missing side lengths. Leave the answers as radicals in the simplest form.


`A) a=(7√(6) )/(2) , b=(7√(3) )/(3) \\\\B) a=7√(2) , b=(7√(3) )/(3) \\\\C) a=(7√(6) )/(2), b=7\\\\D) a=7√(2), b=7`

Answer 1

D

Explanation:

Using trigonometric ratios in the right triangle

tan45° = 1 and cos45° =
`(1)/(√(2) )`

tan45° =
`(opposite)/(adjacent)` =
`(b)/(7)`

Multiply both sides by 7

7 × tan45° = b, that is

b = 7 × 1 = 7

--------------------------------------------------------

cos45° =
`(adjacent)/(hypotenuse)` =
`(7)/(a)`

Multiply both sides by a

a × cos45° = 7, that is

a ×
`(1)/(√(2) )` = 7

Multiply both sides by
`√(2)`

a = 7
`√(2)`