Question

Sec theta =17/8, then find the value of cosec theta, where theta is positive acute angle

Answer 1

as we learn that sec theta = h/b isliye first we find p , h square_b square =15. cosec theta=h/p= 17/15

Answer 2

Value of $\bf cosec \: \theta$ is $\bf \frac{17}{15}$.

Given:

$sec \: \theta = \frac{17}{8}$

To find: Find the value of $cosec \: \theta$, where $\theta$, is positive acute angle.

Solution:

We know that,

$sec \: \theta$ is ratio of hypotenuse to side adjacent to angle $\theta$.

Thus,

Apply Pythagoras theorem to find third side.

Step 1:

See the attached figure for better understanding.

As

$sec \: \theta = \frac{17k}{8k} = \frac{Hypotenuse}{Adjacent \: side} = \frac{BC}{AB}$

So,

AB= 8k units

BC= 17k units

As, k be the common factor of ratio.

Step 2: Apply Pythagoras theorem.

BC²= AB²+CA²

$( {17k)}^{2} = ( {8k)}^{2} + ( {CA)}^{2}$

or

$289{k}^{2} = 64 {k}^{2} + {CA}^{2}$

or

${CA}^{2} = 289 {k}^{2} - 64 {k}^{2}$

or

${CA}^{2} = 225 {k}^{2}$

or

${CA} = 15k$

Step 3: Apply ratio for $\ bf cosec \: \theta$

As

$cosec \: \theta = \frac{Hypotenuse}{Side \: Opposite} = \frac{CB}{CA}$

or

$cosec \: \theta = \frac{17k}{15k}$

Thus,

$\bf cosec \: \theta = \frac{17}{15}$

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