Question

The figure shows triangle ABC with side AC = 4 root 2 units inscribed in a circle of radius 4 units. The length of the arc BDC is 10 pie / 3 units



I have attached the figure with this question. Please answer it fast.

Need each and every step and detailed explanation of every step the theorems as well as all the assumptions assumed.

The fastest and the correct answer would surely be marked as the BRAINLIEST.
by
- Hardwell-

Answer 1

hey mate

here is your solution.....

ANSWER:

A=75°

AB=4√3 units

BC=2.07 units (approx)

EXPLANATION: REFER TO THE ATTACHMENT!

LIKE AS MUCH AS YOU CAN!!!!

Answer 2

Given:

∠ACB = 60°

Arc CDB = 10π/3 units

Radius = 4 units

AC = 4√2 units

To Find:

1) ∠A

2) Length AB and BC

Formulae:

$\text{Length of arc } = \dfrac{\theta}{360} \times 2\pi r$

$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$

Solution

* Refer to the attached drawing for a visual representation of the question.

Find ∠COB:

$\text{Length of arc } = \dfrac{\theta}{360} \times 2\pi r$

$\dfrac{10 \pi}{3} = \dfrac{\theta}{360} \times 2\pi (4)$

$\dfrac{10 \pi}{3} = \dfrac{8\pi \theta}{360}$

$24 \pi \theta = 3600 \pi$

$\theta = 3600 \pi \div 24 \pi$

$\theta =150 ^\circ$

Find ∠A:

Angle at the centre of the circle is twice the angle at the circumference

$\angle \:a = \dfrac{1}{2} \times 150$

$\angle \:a = 75^\circ$

Find ∠B:

Sum of angles in a triangle is 180°

$\angle \:b = 180 - 75 - 60$

$\angle \:b = 45^\circ$

Find Length BC:

$\dfrac{BC}{\sin (75)} = \dfrac{4\sqrt{2} }{\sin (45)}$

$BC = \dfrac{4\sqrt{2} \times \sin(75) }{\sin (45)}$

$BC = 7.73 \text{ units}$

Find Length AB:

$\dfrac{4\sqrt{2} }{\sin (45)} = \dfrac{AB}{\sin (60)}$

$AB = \dfrac{4\sqrt{2} \times \sin(60) }{\sin (45)}$

$AB =6.93 \text { units}$

$\boxed{\text{Answer: } \angle a = 75^\circ , BC = 7.73 \text{ units , } AB = 6.93 \text{ units}}$