sin theta is equal to 24/25 find tan TAN theeta+sec theta
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sin∅ = 24 / 25
Height / hypotenuse = 24 / 25
As 24 / 25 { ratio } is in it's simplest form, we can't take the values directly. So :
Let height of the triangle from ∅ = 24x units
and, hypotenuse of the triangle = 25x units
As trigonometry is applied, given triangle is right angled triangle. Therefore applying Pythagoras theorem,
Base² + Height² = Hypotenuse²
Base² + ( 24x )² = ( 25x )²
Base² = 49x
Base = 7x units
Now,
tan∅ + sec∅
height / base + hypotenuse / base
( height + hypotenuse ) / base
( 24x + 25x ) / 7x
49x / 7x
7
Hence,
Value of tan∅ + sec∅ = 7
Height / hypotenuse = 24 / 25
As 24 / 25 { ratio } is in it's simplest form, we can't take the values directly. So :
Let height of the triangle from ∅ = 24x units
and, hypotenuse of the triangle = 25x units
As trigonometry is applied, given triangle is right angled triangle. Therefore applying Pythagoras theorem,
Base² + Height² = Hypotenuse²
Base² + ( 24x )² = ( 25x )²
Base² = 49x
Base = 7x units
Now,
tan∅ + sec∅
height / base + hypotenuse / base
( height + hypotenuse ) / base
( 24x + 25x ) / 7x
49x / 7x
7
Hence,
Value of tan∅ + sec∅ = 7
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