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Solution for Given 15 cot A = 8. Find sin A and sec A - CBSE Class 10 - Mathematics

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Question

Given 15 cot A = 8. Find sin A and sec A

Solution

Consider a right-angled triangle, right-angled at B.

cot A =`(AB)/(BC)`

`= (AB)/(BC)`

it is given that

cot A = 8/15

`(AB)/(BC)=8/15`

Let AB be 8k.Therefore, BC will be 15k, where k is a positive integer.

Applying Pythagoras theorem in ΔABC, we obtain

AC2 = AB2 + BC2

= (8k)2 + (15k)2

= 64k2 + 225k2

= 289k2

AC = 17k

sin A `= (15k)/(17k) = 15/17`

sec A ` = (AC)/(AB) = 17/8`

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Solution Given 15 cot A = 8. Find sin A and sec A Concept: Trigonometric Ratios of an Acute Angle of a Right-angled Triangle.
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