Question

In triangle ABC, AD is perpendicular to BC.
sin B = 0.8, BD = 9 cm and tan C = 1.
Find the length of AB, AD, AC and DC​​

Answer 1

BD² = 9x²

.. BD = 3x

Now

BD = 9

3x = 9

x = 3

Therefore

AB = 5x

= 5x3

= 15 cm

And

AD= 4x

= 4 x 3

= 12 cm

Chapter 22: Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and their Reciprocals] - Exercise 22And

AD= 4x

= 4 x 3

= 12 cm

Again

1 1 tan C =

i.e. perpendicular base AD DC 1 1 =

Therefore if length of perpendicular

= x, length of base = x

SinceAD² + DC² = AC²... [ Using Pythagoras Theorem ]

(x)² + (x)² = AC²

AC² = 2x²

• AC = √√2x

Now

AD = 12

x = 12

Therefore

DC = x

= 12 cm

And

AC = √2AD = 12

x = 12

Therefore

DC = x

= 12 cm

And

AC = √2

= √2x12

= 12√/2cm