Question

in a right angle triangle it is given that angle a is an acute angle and that tan a is 5/ 12 find the value of cos a​

Answer 1

Given:-

• A right angle triangle such that A is an acute angle and tanA = 5/12.

Find:-

Value of cosA.

Solution:-

Consider a ΔABC such that -

• ∠C = 90°
• tanA = 5/12

BC = 5 cm and AC = 12 cm

Now,

$\bold{\sf{tanA\:=\:\dfrac{P}{B}\:=\:\dfrac{5}{12}}}$

Here..

P = Perpendicular

B = Base

We have given value of Perpendicular and Base. But not of Hypotenuse.

We know that, By Pythagoras Theorem

• (Hypotenuse)² = (Base)² + (Perpendicular)²

Or

• H² = P² + B²

Substitute the known values in above formula to find the value of Hypotenuse (H).

=> (H)² = (5)² + (12)²

=> (H)² = 25 + 144

=> (H)² = 169

=> H = √169

=> H = 13 cm

So, by Pythagoras Theorem we have Hypotenuse (H) = 13

Now, we have to find the value of cosA.

$\bold{\sf{cosA\:=\:\dfrac{B}{H}}}$

From above calculations we have B (Base) = 5 and H (Hypotenuse) = 13

So,

$\bold{\sf{cosA\:=\:\dfrac{B}{H}\:=\:\dfrac{12}{13}}}$

Answer 2

ANSWER IS IN THE ATTACHMENT I GAVE:-

EXPLANATION:-

WE ARE GIVEN THE VALUT TAN (a) AND BY USING IT WE CAN FIND THE VALUE OF HYPOTENUSE OF THE TRIANGLE.

USKE BAAD.....XD

THEN WE KNOW THAT CAS THETA =b/h AND SIMILARLY SUBSTITUTING THE VALUE WE GET COS a =12/13