Question

${\underline{\underline{\red{\pmb{\sf{ Solve \; :- }}}}}}$

$\longmapsto$ In the given ∆ABC it is given that $\angle$ B = 90° .AB = 24 cm and BC = 7 cm than find the Value of Cos A = ? .



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Answer 1

Answer:

HEY MATE THIS IS YOUR ANSWER

In this answer I find the value of COS A, and SIN A.

Answer 2

Given :-

• Triangle ABC with

Angle B as 90°

AB as 24 cm

BC as 7 cm

To find :-

• The value of Cos A

Concept :-

We need to find the Cos A [ Cos of Angle A ] . For Angle A base is AB , perpendicular is BC and Hypotenuse is AC . As Cos θ = $\sf \frac{Base}{Hypotenuse}$ So we need Base and Hypotenuse , we know the value of Base [ AB ] but we don't know the value of Hypotenuse [ AC ] ∴ We will take first the value of AC by Pythagoras theorem . Then we can easily find the value of Cos A .

Solution :-

Applying Pythagoras theorem for derivation of Hypotenuse [ AC ]

$\longrightarrow \sf {AC}^{2} = {AB}^{2} + {BC}^{2}$

$\longrightarrow \sf {AC}^{2} = {24}^{2} + {7}^{2}$

$\longrightarrow \sf {AC}^{2} = 576 + 49$

$\longrightarrow \sf {AC}^{2} = 625$

$\longrightarrow \sf AC = \sqrt{625}$

$\longrightarrow \sf AC = \sqrt{ {25}^{2} }$

$\longrightarrow \sf AC = 25$

Now ,

Calculating the value of Cos A

As we know ,

$\star\:{\underline{\boxed{\rm{\purple{ Cos \: θ \: =\sf \frac{Base}{Hypotenuse} }}}}}⋆$

$∴ \sf \: Cos \: A = \dfrac{AB}{AC}$

$\longrightarrow\sf \: Cos \: A = \dfrac{24}{25}$

Therefore ,

$\star\:{\underline{\boxed{\rm{\red{ Cos \: A = \dfrac{24}{25} }}}}}⋆$

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