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Answer 1

Given :-

BC = 15cm and Sin B = 4/5

Solution 1 :-

As we know,

Sin Φ = Perpendicular / Hypotenuse

Therefore

Sin B = 4/5

Let the perpendicular and sides be 4x and 5x

So , AC = 4x and BD = 5x

By using Pythagoras theorem,

(AB)^2 = (AC)^2 + (BC)^2

(5)^2 = ( 4x)^2 + (BC)^2

(5x)^2 - ( 4x)^2 = ( BC)^2

As we know, BC = 15cm

25x^2 - 16x^2= 225

9x^2 = 225

x^2 = 225/9

x^2 = 25

x = 5

Now,

AC = 4 * 5 = 20cm

AB = 5 * 5 = 25cm

Given :-

TanΔADC = 1

Solution 2 :-

As we know that,

Tan Φ = Perpendicular / base

Tan ΔADC = 1 / 1

Therefore,

Perpendicular AC = x and base CD = x

Now, As we know that

AC = 20cm

Therefore,

CD = 20cm

Now,

Tan B = AC / BC = 20/15 = 4/3

Cos B = BC / AB = 15/25 = 3 / 5

So,

Tan^2 B - 1/ Cos^2B

( 4/3)^2 - 1/ ( 3/5)^2

16/9 - 25/9

= - 9/9

= -1

Hence, Tan^2B - 1/Cos^2B = -1$.$

Answer 2

Step-by-step explanation:

1. (i)

⇒sinB= AC/AB = WHOLE ROOT AB²−BC²/AB

⇒ 4/5AB= WHOLE ROOT AB²−15²

⇒16AB²=25AB²−(25)(15)³

⇒AB²= 925×15×15

⇒ AB=25

hope it is helpful