50 points find the side and length of the rectangle. The answers are shown in faded ink, can anyone explain the steps of tan to find the side and length of the rectangle. 50 points shown on 2nd page of my questions in repeat same question.

The value of BD is 6√3 cm and BF = 3√3 cm

Step-by-step explanation:

Firstly, we have to find the length of BD using Tangent Rule, tanθ = oppo./adj. :

θ = 60°

adj. = 6 cm

oppo. = BD

tan 60° = BD/6

BD = 6 tan 60°

= 6√3 cm

Next, we have to find the length of BF but we have to find the angle of BAF first. In order to find the angle of BAF, we have to substract ∠ACE and ∠AEC from 180° as the total interior angle for triangle is 180° :

∠CAE + ∠ACE + ∠AEC = 180°

∠CAE + 60° + 90° = 180°

∠CAE = 180° - 90° - 60°

= 30°

∠BAF = ∠CAE = 30°

θ = 30°

oppo. = BF

adj. = 9 cm

tan 30° = BF/9

BF = 9 tan 30°

= 3√3 cm

see below

Step-by-step explanation:

We can find the length of BD

tan theta = opp side/ adj side

tan 60 = BD / 6

6 tan 60 = BD

6 sqrt(3) = BD

The large triangle is a 30 60 90  (sin we know it is a right angle and the top is 60, Angle A must be 30  (180-90-60 = 30)

We can find BF

tan 30 = opp side/ adj side

tan 30 = BF /9

9 tan 30 = BF

9 * sqrt(3)/3 = BF

3 sqrt(3) = BF

The perimeter of the rectangle is

P = 2(l+w)

The length is  BD and the width is BF

P = 2( 6 sqrt(3) + 3 sqrt(3))

  = 2 (9 sqrt(3))

   18 sqrt(3)

The area is

A = l*w

  = 6 sqrt(3)* 3 sqrt(3)

18 sqrt(3*3)

18 (3)

  54

b

step-by-step explanation: