Question

Refer to right triangle ABC in which \(C = 90^{\circ}.\) Solve each triangle.
\(a = 4.37,\ c = 6.21\)

Answer 1

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)