131k views
2 votes
Find the tangent of

Find the tangent of-example-1

1 Answer

2 votes

Check the picture below.


\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{√(21)}\\ a=\stackrel{adjacent}{YZ}\\ o=\stackrel{opposite}{3} \end{cases} \\\\\\ (√(21))^2= (YZ)^2 + (3)^2\implies 21=YZ^2+9 \\\\\\ 12=YZ^2 \implies √(12)=YZ \\\\[-0.35em] ~\dotfill


\tan(Y )=\cfrac{\stackrel{opposite}{3}}{\underset{adjacent}{√(12)}}\implies \tan(Y )=\cfrac{3}{√(12)}\cdot \cfrac{√(12)}{√(12)}\implies \tan(Y )=\cfrac{3√(12)}{12} \\\\\\ \tan(Y )=\cfrac{3√(2^2\cdot 3)}{12}\implies \tan(Y )=\cfrac{6√(3)}{12}\implies \tan(Y )=\cfrac{√(3)}{2}

Find the tangent of-example-1
User Jeevanantham
by
7.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories