Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Suppose each edge of the cube shown in the figure is 10 inches long. Find the sine and cosine of the angle formed by diagonals DE and DG.

Suppose Each Edge Of The Cube Shown In The Figure Is 10 Inches Long Find The Sine And Cosine Of The Angle Formed By Diagonals DE And DG class=

Sagot :

Check the picture below.

[tex]sin(EDG )=\cfrac{\stackrel{opposite}{10}}{\underset{hypotenuse}{10\sqrt{3}}}\implies sin(EDG )=\cfrac{1}{\sqrt{3}}\implies sin(EDG )=\cfrac{1}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{sin(EDG )=\cfrac{\sqrt{3}}{\sqrt{3^2}}\implies sin(EDG )=\cfrac{\sqrt{3}}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]cos(EDG )=\cfrac{\stackrel{adjacent}{10\sqrt{2}}}{\underset{hypotenuse}{10\sqrt{3}}}\implies cos(EDG )=\cfrac{\sqrt{2}}{\sqrt{3}}\implies cos(EDG )=\cfrac{\sqrt{2}}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{cos(EDG )=\cfrac{\sqrt{6}}{\sqrt{3^2}}\implies cos(EDG )=\cfrac{\sqrt{6}}{3}}[/tex]

View image jdoe0001
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.