Question

Find the missing side of the triangle SHOW YOUR WORK!!

Answer 1

139.49

Step-by-step explanation:

using trig ratios.

tan=o/a

tan74°=n/40

40tan74°=n

use calculator to solve

=139.49

hope this helped :)

Answer 2

We will solve it using trigonometry formulas:

$\boxed{ \begin{minipage}{5 cm} {Formulae:} \\ \\ \bigstar\:\:\sin\theta\:=\:\frac{Opposite}{Hypotenuse} \\ \\ \bigstar\:\:\cos\theta\:=\:\frac{Adjacent}{Hypotenuse} \\ \\ \bigstar\:\:\tan\theta\:=\:\frac{Opposite}{Adjacent} \end{minipage} }$

$\rule{190pt}{2pt}$

$\bold{\ttt{Given,}}$

$\sf{Adjacent=40}\\ \sf{Opposite=n}\\ \sf{\theta=74\°$

$\bold{\ttt{Solution,}}$

${\tan\theta\:=\:\frac{Opposite}{Adjacent}}}$

${\sf{\tan74\:=\:\frac{n}{40}$

${\sf{\tan74\:x\:40\:=\:n$

${\sf{139.49\:=\:n$

${\sf{n\:\approx139.5$

$\boxed{\sf{n\:=\:139.5}}$