Answer:
m∠C = 72°
BA = 8.6
AC = 2.8
Step-by-step explanation:
We can start by finding the sum of all angles in a triangle to find angle C. The sum of all angles is 180°, so we can write the equation:
m∠A + m∠B + m∠C = 180°
And substitute what we have:
90° + 18° + m∠C = 180°
108° + m∠C = 180°
m∠C = 72°
In order to find the side BA, we can use trig functions. We are given the hypotenuse and we are looking for the side adjacent to ∠B. The trig function that relates the two is cosine. We can set up the equation as follows:
cos(∠B) = [tex]\frac{BA}{BC}[/tex]
cos(18°) = [tex]\frac{BA}{9}[/tex]
9 * cos(18°) = BA
BA ≈ 8.559508647
And when we round, we get:
BA = 8.6
In order to find the side AC, we can use trig functions. We are given the hypotenuse and we are looking for the side opposite to ∠B. The trig function that relates the two is sine. We can set up the equation as follows:
sin(∠B) = [tex]\frac{AC}{BC}[/tex]
sin(18°) = [tex]\frac{AC}{9}[/tex]
9 * sin(18°) = AC
AC ≈ 2.781152949
We can round this to:
AC = 2.8
