Answer:
The measures of all angles are [tex]30\°,60\°,90\°[/tex]
Step-by-step explanation:
we know that
In a right triangle
Applying the Pythagoras theorem
[tex]c^{2}=a^{2}+b^{2}[/tex]
where
c is the hypotenuse
a,b are the legs
In this problem we have
[tex]c=8\ units, a=4\ units[/tex]
Find the value of b
[tex]8^{2}=4^{2}+b^{2}[/tex]
[tex]b^{2}=8^{2}-4^{2}[/tex]
[tex]b^{2}=48[/tex]
[tex]b=4\sqrt{3}\ units[/tex]
Remember that
A right triangle has a right angle and the other two angles are complementary
Let
[tex]\alpha[/tex] ------> one of the two angles that are complementary
[tex]\theta[/tex] ------> the second of the two angles that are complementary
so
[tex]\alpha=arccos(a/c)=arccos(4/8)=60\°[/tex]
[tex]\theta=arccos(b/c)=arccos(4\sqrt{3}/8)=30\°[/tex]
The measures of all angles are [tex]30\°,60\°,90\°[/tex]
