To solve the question we have to draw the triangle with the given information
Since the sum of the angles of any triangle is 180 degrees, then
Subtract [tex]\begin{gathered} m\angle B=180-25-90 \\ m\angle B=65^{\circ} \end{gathered}[/tex]We will use the trigonometry ratios to find a, b
[tex]\begin{gathered} \sin A=\frac{a}{c} \\ \cos A=\frac{b}{c} \end{gathered}[/tex]Since c = 80, then
[tex]\sin (25)=\frac{a}{80}[/tex]By using cross multiplication
[tex]\begin{gathered} a=80\sin (25) \\ a=33.81m\rightarrow(2d.p) \end{gathered}[/tex][tex]\begin{gathered} \cos (25)=\frac{b}{80} \\ b=80\cos (25) \\ b=72.50m\rightarrow(2d.p) \end{gathered}[/tex]The missing in the triangles are:
m
a = 33.81 to the nearest 2 d.p
b = 72.50 to the nearest 2 d.p
