Question

if 17sinA=8,find the values of CosA and tanA

Answer 1

GIVEN:

• 17sinA = 8

TO FIND:

• What is the value of CosA and TanA ?

SOLUTION:

We have,

⠀⠀⠀17sinA = 8

$\implies$ sinA = 8/17

In right ∆POM

$\bf\red{sinA = \frac{Perpendicular}{Hypotenuse} = \frac{PM}{PO}}$

If PO = 17k, then PM = 8k, where k is a positive number.

Using Pythagoras theorem:

$\rm\red{ (Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2 }$

$\implies$$\rm{ (PO)^2 = (OM)^2 + (PM)^2<strong> </strong>}$

$\implies$$\rm{ (17k)^2 = (OM)^2 + (8k)^2}$

$\implies$$\rm{ {(17k)}^{2} - {(8k)}^{2} = {(OM)}^{2 }}$

$\implies$$\rm{ 289k - 64k = (OM)^2}$

$\implies$$\rm{ 225k = OM^2}$

$\implies$$\rm{ 15k = OM}$

Thus,

$\bf\red{CosA = \frac{Base}{Hypotenuse}}$

$\implies$ $\rm{CosA = \frac{15}{17}}$

$\bf\red{TanA = \frac{Perpendicular}{Base} }$

$\implies$$\rm{ TanA =\frac{ 8}{15}}$

❛ Hence, Cos A = 15/17

TanA = 8/15 ❜ 

_________________

Answer 2

Answer:

CosA = base/hypothenuse = 15/17

TanA = perpendicular/hypothenuse = 8/15

$\large\underline\mathrm{Given:-}$

$\implies$ 17sinA = 8

$\large\underline\mathrm{To \: find}$

What is the value of CosA and TanA ?

$\large\underline\mathrm{Solution}$

$\implies$ 17sinA = 8

$\implies$ sinA = 8/17

$\implies$ perpendicular = 8

$\implies$ hypotenuse = 17

$\implies$ base = ?

• Using Pythagoras theorem:

$\implies$ h² = p² + b²

$\implies$ 17² = 8² + b²

$\implies$ b² = 289 - 64

$\implies$ b² = 225

$\implies$ b = 15

Thus,

CosA = base/hypothenuse = 15/17

TanA = perpendicular/hypothenuse = 8/15