The angle A is given 72 degree and angle C is given 90 degree.
The side b is 5.
Then the right triangle is given
Use the property , the sum of the angles of the property is the 180 degree.
[tex]90^{\circ}+72^{\circ}+\angle B=180^{\circ}[/tex][tex]\angle B=180^{\circ}-90^{\circ}-72^{\circ}[/tex][tex]\angle B=18^{\circ}[/tex]
Then the angle B is 18 degree.
Then to determine side a , use the tan trigonometric function.
[tex]\tan 72^{\circ}=\frac{a}{5}[/tex][tex]a=5\times tan72^{\circ}=15.38[/tex]
The side a is 15.38.
Now to determine the side c, use the trigonometric function sin .
[tex]\sin 72^{\circ}=\frac{a}{c}=\frac{15.38}{c}[/tex][tex]c=\frac{15.38}{\sin 72^{\circ}}=16.18[/tex]
The side c is 16.18.
