Answer:
Part 1) The length of the hypotenuse is 10 cm
Part 2)The length of the other leg is 6 cm
Step-by-step explanation:
step 1
Find the length of the hypotenuse
Let
x -----> the length of the other leg
y -----> the length of the hypotenuse
A -----> the angle opposite to the leg equal to 8 cm
we know that
[tex]sin(A)=8/y[/tex]
we have
[tex]sin(A)=0.8[/tex]
substitute
[tex]0.8=8/y[/tex]
Solve for y
[tex]y=8/0.8[/tex]
[tex]y=10\ cm[/tex]
therefore
The length of the hypotenuse is 10 cm
step 2
Find the length of the other leg
Let
x -----> the length of the other leg
y -----> the length of the hypotenuse
we know that
Applying the Pythagoras Theorem
[tex]y^{2}=x^{2}+8^{2}[/tex]
we have
[tex]y=10\ cm[/tex]
substitute and solve for x
[tex]10^{2}=x^{2}+8^{2}[/tex]
[tex]100=x^{2}+64[/tex]
[tex]x^{2}=100-64[/tex]
[tex]x^{2}=36[/tex]
[tex]x=6\ cm[/tex]
