Data analysis

Given \(\triangleABC\) is a right angled triangle at C.

And \(a = 4.37\) units

\(c = 6.21\) units

To solve the triangle.

The triangle is as follows,

Solution

Since the triangle is right angle,

\(\sin\ A = \frac{opposite\ side}{hypotenuse}\)

\(= BC/AB\)

\(= a/c\)

\(= 4.37/6.21\)

\(\Rightarrow\ A = \arcsin\ (704)\)

\(\Rightarrow\ \angle\ A = 44.75^{\circ}\)

(Rounded to two decimals)

Sum of all angles in a triangle \(= 180^{\circ}\)

\(\Rightarrow\ \angle\ A\ +\ \angle\ B\ +\ \angle\ C = 180^{\circ}\)

\(\Rightarrow\ 44.75^{\circ}\ +\ \angle\ B\ +\ 90^{\circ} = 180^{\circ}\)

\Rightarrow\ \angle\ B = 45.25^{\circ}\)

Since the triangle is right angle,

\(\cos\ A = \frac{adjacent\ side}{hypotenuse}\)

\(= AC/AB\)

\(= b/c\)

\Rightarrow\ b = 6.21 (\cos\ 44.75^{\circ})\)

\(= 6.21 (0.710185376)\)

\Rightarrow\ b = 4.41\) units

(Rounded to two decimals)