Question

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

Answer 1

We will solve it using trigonometry formulas:

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

`\rule{190pt}{2pt}`

`\bold{\ttt{Given,}}\\`

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

`\bold{\ttt{Solution,}}\\`

`{\tan\theta\:=\:(Opposite)/(Adjacent)}}`

`{\sf{\tan74\:=\:(n)/(40)`

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

`{\sf{139.49\:=\:n`

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

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

Answer 2

139.49

Explanation:

using trig ratios.

tan=o/a

tan74°=n/40

40tan74°=n

use calculator to solve

=139.49

hope this helped :)