Question

Please answer this question ​

Answer 1

Answer:

Option (a) is correct

Step-by-step explanation:

Given that ABCD is a rectangle.

Therefore, AD = BC = 40 cm ( since opposite sides of a rectangle are always equal ).

Now, consider ∆ ADE

⇒ cos θ = base/hypo.

⇒ cos 60° = AD/AE

⇒ 1/2 = 40/AE ‎ ‎ ‎ ‎ ‎ ‎ [ ∵ cos 60° = 1/2 ]

⇒ AE = 2(40)

⇒ AE = 80

Therefore, length of AE is 80 units.

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Additional Information :-

• sin A = Perpendicular / Hypotenuse
• tan A = Perpendicular / base
• cosec A = Hypotenuse / Perpendicular

• sec² A - tan² A = 1
• 1 + cot² A = cosec²A
• sin² A + cos² A = 1

• sin ( 90° - A ) = cos A
• cos ( 90° - A ) = sin A
• tan ( 90° - A ) = cot A
• cot ( 90° - A ) = tan A
• cosec ( 90° - A ) = sec A
• sec ( 90° - A ) = cos A

Answer 2

The value of AE is equal to (a) 80 units.

Step-by-step explanation:

We are given a rectangle ABCD having length and breadth as 90 and 40 units respectively. AE is a line is taken from point A having angles,

$\angle DAE=60\°$

$\angle BAE=30\°$  

and we have to find the value of AE.

• Formula used,

$Cos\theta=\frac{b}{h}$

b is for the base and h for hypotenuse.  

• Calculation for AE,

As we can see ADE forming a right angled triangle having right angle at D. In this $\triangle ADE$ , side AD is given to us as and $\angle DAE$ is also given to us.

$AD=40units$

$\angle DAE=60\°$

as we have only AD that's why we use $Cos\theta$  formula here because AD is a base for angle $\angle DAE=60\°$ .

so the $\theta=60\°$  here ,

$Cos\theta=\frac{b}{h}$

$b=40$

$h=AE$

$Cos60\°=\frac{40}{h}$

and the value of $Cos60\°=\frac{1}{2}$

$\frac{1}{2} =\frac{40}{h}$

doing Cross multiplication to get the value of h,

$h=2*40$

$h=80$

as $h=AE$ so $AE=80units$.

 In this way we get the answer of this question as $AE=80units$.