# Given 15 cot A = 8, find sin A and sec A

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

Given: 15 cot A = 8
To find: sin A and sec A

Cot A =

It is given that,

Cot A =

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

Pythagoras Theorem: It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Applying Pythagoras theorem in ΔABC, we obtain

AC2 = AB2 + BC2

= (8k)2 + (15k)2

= 64k2 + 225k2

= 289k2

AC = 17k

Now we know that,

Sin A =

=

And also,

Sec A =

=

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