Answer:
[tex]c = 3.6[/tex]
[tex]A = 56.4^\circ[/tex]
[tex]B = 33.6^\circ[/tex]
Step-by-step explanation:
Given
See attachment
Solving (a): Segment C
To do this, we make use of Pythagoras theorem
[tex]c^2 =a^2 + b^2[/tex]
[tex]c^2 =2^2 + 3^2[/tex]
[tex]c^2 = 4 + 9[/tex]
[tex]c^2 = 13[/tex]
Take the square root of both sides
[tex]c = \sqrt{13[/tex]
[tex]c = 3.6055[/tex]
[tex]c = 3.6[/tex] --- Approximate
Solving (b): Measure of A
To do this, we make use of:
[tex]sin\ A = \frac{Opposite}{Hypotenuse}[/tex]
This gives:
[tex]sin\ A = \frac{3}{3.6}[/tex]
[tex]sin\ A = 0.8333[/tex]
Take arcsin of both sides
[tex]A = sin^{-1}(0.8333)[/tex]
[tex]A = 56.4^\circ[/tex]
Solving (c): The measure of C
This is calculated as:
[tex]A + B + 90^\circ = 180^\circ[/tex]
So, we have:
[tex]B = 180^\circ - 90^\circ - 56.4^\circ[/tex]
[tex]B = 33.6^\circ[/tex]
