Question

hi friend please help me with this iam In a harry

In given figure CD=40 and angle ADB= 45 and angle ACB=60 calculate the length of AB and BC

NOTE:- THERE IS NO MISTAKE IN THE QUESTION
IF THE ANSWER IS CORRECT I WILL MARK AS BRAINLIEST AND I PROMISE

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

As in the figure

Assume AB = h and BD = x

★Now in Triangle ABD :-

★We know that :-

$\tt{\rightarrow tan\theta=\dfrac{Perpendicular}{Base}$

${\boxed{tan60=\dfrac{h}{x}}$

★Hence :-

h = √3x ....... (1)

★Now in Triangle ABC :-

${\boxed{tan45=\dfrac{h}{x+40}}$

★We know that (tan45 = 1)

h = x + 40 ...... (2)

★Now substitute of value of (2) in (1) we get :-

√3x = 40 + x

√3x - x = 40

x(√3 - 1) = 40

$\tt{\rightarrow x=\dfrac{40}{\sqrt{3}-1}$

★Or,

$\tt{\rightarrow x=\dfrac{40}{\sqrt{3}-1}\times\dfrac{\sqrt{3}+1}{\sqrt{3}+1}}$

x = 20(√3 + 1)

★Now substitute the value of x in (1)

h = √3x

h = √3 × 20(√3 + 1)

h = 20√3(√3 + 1)

★Or,

$\tt{\rightarrow h=\dfrac{40\sqrt{3}}{(\sqrt{3}-1)}}$