Question

please help me thank you so much

Answer 1

Answer:

Solving for d :

» We're gonna use the sine trigonometric ratios angle 60°

${ \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }} \\ \\ { \tt{ \sin(60 \degree) = \frac{d}{2} }} \\ \\ { \tt{d = 2 \times \sin(60 \degree) }} \\ { \tt{d = 2 \times \frac{ \sqrt{3} }{2} }} \\ \\ { \boxed{ \tt{ \: d = \sqrt{3} } \: }}$

Solving for b :

» We're gonna use cosine trigonometric ratios of angle 45°

${ \tt{ \cos( \theta) = \frac{adjacent}{hypotenuse} }} \\ \\ { \tt{ \cos(45 \degree) = \frac{b}{4} }} \\ \\ { \tt{b = 4 \times \cos(45 \degree) }} \\ { \tt{b = 4 \times \frac{1}{ \sqrt{2} } = \frac{4}{ \sqrt{2} } }} \\ \\ { \tt{b = ( \frac{4}{ \sqrt{2} }) \times \frac{ \sqrt{2} }{ \sqrt{2} } }} \\ \\ { \tt{b = \frac{4 \sqrt{2} }{2} }} \\ \\ { \boxed{ \tt{ \: b = 2 \sqrt{2} \: }}}$