Question

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

Answer 1

Answer:

D

Step-by-step explanation:

Using trigonometric ratios in the right triangle

tan45° = 1 and cos45° = $\frac{1}{\sqrt{2} }$

tan45° = $\frac{opposite}{adjacent}$ = $\frac{b}{7}$

Multiply both sides by 7

7 × tan45° = b, that is

b = 7 × 1 = 7

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

cos45° = $\frac{adjacent}{hypotenuse}$ = $\frac{7}{a}$

Multiply both sides by a

a × cos45° = 7, that is

a × $\frac{1}{\sqrt{2} }$ = 7

Multiply both sides by $\sqrt{2}$

a = 7$\sqrt{2}$