Answer:
Part 1) [tex]c=21.9\ units[/tex]
Part 2) [tex]B=61.1\°[/tex]
Part 3) [tex]A=28.9\°[/tex]
Part 4) [tex]C=90\°[/tex]
Step-by-step explanation:
step 1
Find the length side c
Applying the Pythagoras Theorem
[tex]c^{2}=a^{2}+b^{2}[/tex]
substitute the given values
[tex]c^{2}=10.6^{2}+19.2^{2}[/tex]
[tex]c^{2}=481[/tex]
[tex]c=21.9\ units[/tex]
step 2
Fin the measure of angle B
we know that
In the right triangle
[tex]tan(B)=b/a[/tex]
substitute the given values
[tex]tan(B)=19.2/10.6[/tex]
[tex]B=arctan(19.2/10.6)=61.1\°[/tex]
step 3
Find the measure of angle A
we know that
The measure of interior angles in a triangle must be equal to 180 degrees
so
∠A+∠B+∠C=180°
Remember that in a right triangle the measure of angle C is 90 degrees
we have
[tex]B=61.1\°[/tex]
[tex]C=90\°[/tex]
substitute
[tex]A+61.1\°+90\°=180\°[/tex]
[tex]A=28.9\°[/tex]
