Answer:
See below for an explanation
Step-by-step explanation:
I'm unsure of your answer choices, so I'll show you how to solve for the remainder of the whole triangle:
Since we are given a hypotenuse of 5 and a side length of 4 which is adjacent to ∅, the trig function to solve for ∅ would be cosine because cos∅=adjacent/hypotenuse (SOHCAHTOA). This means cos∅=4/5 and taking the arccos (the inverse of cosine aka. cos^-1) of both sides gets us ∅=36.87°
Side AC can be solved by using the Pythagorean Theorem since a²+b²=c² can be turned into 4²+b²=5². We would then have 16+b²=25 which is also b²=9, thus taking the square root of both sides gives us b=3 (since distance is positive). Thus, side AC has a length of 3 units.
∠A can be found by using the Triangle Angle-Sum Theorem. Since all the interior angles of a triangle must add up to 180°, then ∠A+∠B+∠C=180°. We know that since ∠B=36.87° and ∠C=90°, then we have the equation ∠A+36.87°+90°=180°. Combining like terms on the left side gets us ∠A+126.87°=180° and subtracting on both sides get us ∠A=53.13°
<u>Final sides and angles of the triangle:</u>
∠A=53.13°
∠B=36.87°
∠C=90°
BC=4
BA=5
AC=3
