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bhobarnob

· started a discussion

· 1 Months ago

could some one please explain (Question: 388255.0 )

i didn't understand the soln. please help

Question:

In the figure given below, ABC is right angled at B and ∆ABD is right angled at A. If BD is perpendicular to AC and BC =  23    cm with ∠CAB = 30°, then the length of AD is 

   

Options:
A)

53    cm

B)

43    cm

C)

73    cm

D)

63    cm

Solution:

Ans: (d)

  

isha mishra

· commented

· 1 Months ago

First, look into the right triangle ABC,

It is given in the question that BE is perpendicular to the hypotenuse AC; there is a property of right triangle for this condition as follows:

AE = AB2/AC

2 IN THE ABOVE PROPERTY IS SQUARE i.e. AE = SQUARE OF AB UPON AC

You can easily find AB AND AC, so just put the values:

AE = 6*6 /4root 3

= 3root3

Now, look into the right triangle DEA,

angle DAE = 90-30 = 60

Just apply cos60 = AE/AD

1/2 = 3root3 / AD

AD = 6ROOT3.........THE ANSWER
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