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

[tex]A) a=\frac{7\sqrt{6} }{2} , b=\frac{7\sqrt{3} }{3} \\\\B) a=7\sqrt{2} , b=\frac{7\sqrt{3} }{3} \\\\C) a=\frac{7\sqrt{6} }{2}, b=7\\\\D) a=7\sqrt{2}, b=7[/tex]

Find the missing side lengths Leave the answers as radicals in the simplest form texA afrac7sqrt6 2 bfrac7sqrt3 3 B a7sqrt2 bfrac7sqrt3 3 C afrac7sqrt6 2 b7D a7 class=

Respuesta :

Answer:

D

Step-by-step explanation:

Using trigonometric ratios in the right triangle

tan45° = 1 and cos45° = [tex]\frac{1}{\sqrt{2} }[/tex]

tan45° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{b}{7}[/tex]

Multiply both sides by 7

7 × tan45° = b, that is

b = 7 × 1 = 7

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cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{7}{a}[/tex]

Multiply both sides by a

a × cos45° = 7, that is

a × [tex]\frac{1}{\sqrt{2} }[/tex] = 7

Multiply both sides by [tex]\sqrt{2}[/tex]

a = 7[tex]\sqrt{2}[/tex]

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