Question

in triangle abc angle a is equal to 90 as is perpendicular to bc and angle b is equal to 46 if ab is equal to x find ad in terms of x ​

Answer 1

Answer:

$\frac{x}{\sqrt{2} }$

Step-by-step explanation:

AD =  x units                                                               .......(i)

Let AD be the perpendicular, BD be the base and AB be the hypotenuse.

∠DAB+∠DBA+∠ADB = 180° ( Sum of all angles of a triangle. )

∠DAB+45°+90° = 180°

∠DAB + 135° = 180° => ∠DAB = 180°-135°

∠DAB = 45°

sin 45° = $\frac{Perpendicular}{hypotenuse}$ => sin 45° = $\frac{AD}{AB}$

$\frac{1}{\sqrt{2} }$  = $\frac{x}{AB}$

On cross multiplication, we get:

AB = $\frac{x}{\sqrt{2} }$