Given 15 cot A = 8, find sin A and sec A.
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10th
Maths
Introduction to Trigonometry
Trigonometric Ratios
Given 15 cot A = 8 , find s...
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Asked on November 22, 2019 by
Täñü Hiran
Given 15cotA=8, find sinA and secA.
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ANSWER
Given,
15cotA=8
cotA=
15
8
=> tanA=
8
15
-------(tanA=
cotA
1
)
We know that,
tanθ=
adjacentSide
oppositeSide
Consider the attached figure, triangleABC
From Pythagoras theorem,
AC
2
=AB
2
+BC
2
AC
2
=8
2
+15
2
=64+225=289
AC=17
cosA=
Hypotenuse
adjacentSide
=
AC
AB
=
17
8
secA=
cosA
1
=
17
8
1
8
17
sinA=
Hypotenuse
oppositeSide
=
AC
BC
=
17
15
15 cot A =8
cot A= 8/15
cot A = 8/15 = base/height
Let height be 15x and base be 8x
______________________________________________
By Pythagoras Theorem,
(15x)^2 + (8x)^2 = hypotenuse^2
(225 + 64)x^2 = hypotenuse^2
289x^2 = hypotenuse^2
17x = hypotenuse
_______________________________________________
Now,
sin A = height/hypotenuse
Sin A = 15/17
AND
sec A = hypotenuse/base
Sec A = 17/8