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

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 $△ A B C$ 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,
$\sin A = \frac{o p p o s i t e s i d e}{h y p o t e n u s e}$
$= B C / A B$
$= a / c$
$= 4.37 / 6.21$
$\Rightarrow A = \arcsin (704)$
$\Rightarrow ∠ A = {44.75}^{\circ}$
(Rounded to two decimals)
Sum of all angles in a triangle $= 180^{\circ}$
$\Rightarrow ∠ A + ∠ B + ∠ C = 180^{\circ}$
$\Rightarrow {44.75}^{\circ} + ∠ B + 90^{\circ} = 180^{\circ}$
$\Rightarrow ∠ B = {45.25}^{\circ}$
Since the triangle is right angle,
$\cos A = \frac{a d j a c e n t s i d e}{h y p o t e n u s e}$
$= A C / A B$
$= b / c$
$\Rightarrow b = 6.21 (\cos {44.75}^{\circ})$
$= 6.21 (0.710185376)$
$\Rightarrow b = 4.41$ units
(Rounded to two decimals)

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

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