Question

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

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

2021-02-16

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)