Math, asked by TGMRohit, 1 month ago

Given A is an acute angle and 13sin A = 5 evaluate : (5sin A - 2cos A)/(tan A) (trigonometry ratios) ​

Answers

Answered by anku7602
1

Answer:

answers

Step-by-step explanation:

(5sinA-2cosA)/tanA

=(5×5/13 - 2×12/13)5/12

=(25/13 - 24/13)5/12

=(1/13)/(5/12)

=(1×12)/(13×5)

=12/65

Answered by Anonymous
4

Answer:

Given : A is an acute angle

13Sin A = 5

To find : (5sin A - 2cos A )/( tan A )

Solution :

13Sin A = 5

Or Sin A = \dfrac{5}{13}

We know that Sin A = \dfrac{Perpendicular}{Hypotenuse}

Thus , Perpendicular = 13 units and Hypotenuse = 5 units

By using Pythagorean theorem ,

H² = P² + B²

(13)² = 5² + B²

169 - 25 = B²

144 = B²

B = √144

B = 12 units

Cos A = \dfrac{Base}{Hypotenuse}

Cos A = \dfrac{12}{13}

Tan A = \dfrac{Perpendicular}{Base}

Tan A = \dfrac{5}{12}

Evaluate : (5sin A - 2cos A)/(tan A)

= 5 × \dfrac{5}{13} - 2 × \dfrac{12}{13}

= \dfrac{25}{13}\:-\:\dfrac{24}{13}

= \dfrac{1}{13}

Now divide it by Tan A that is 5/12

= \dfrac{\frac{1}{13}}{\frac{5}{12}}

= \dfrac{1\:\times\:12}{5\:\times\:13}

= \dfrac{12}{65}

Similar questions