Question

2. Find b 5.0 35° 3. Find a & θ 9.5 84° 1.0 4. Find φ, θ, & c 4.0 3.0

Answer 1

2)
  For the triangle, we have
     $\frac{b}{5}=\cos 35^\circ$
  $\Rightarrow b=5\times \cos 35^\circ = 4.0958$

3)
From the definition of the sine, we have
     $\frac{a}{9.5}=\sin 84^\circ$
  $\Rightarrow a=9.5\times \sin 84^\circ = 9.448$
And for the right angle triangle, we have
   $\theta+84^\circ=90^\circ$
$\Rightarrow \theta=90^\circ-84^\circ$
$\Rightarrow \theta=6^\circ$

4)
From the definition of the tangent, we have
     $\tan\phi=\frac{3}{4}$
  $\Rightarrow \phi=\tan^{-1}\frac{3}{4}$
$\Rightarrow \phi=36.87^\circ$

And for the right angle triangle, we have
   $\theta+\phi=90^\circ$
And so,
   $\Rightarrow \theta=90^\circ-\phi$
  $\Rightarrow \theta=90^\circ-36.87^\circ$
  $\Rightarrow \theta=53.13^\circ$

And from Pythagorus theorem, we have
   $c^2=3^2+4^2$
  $\Rightarrow c^2=9+16$
$\Rightarrow c^2=25$
  $\Rightarrow c=\sqrt{25}$
  $\Rightarrow c=5$