Question

Given 15cot A =8, find sin A and sec A
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Answer 1

15 cot A = 8

cot A = 8/15 = Adjacent side/Opposite side

So, Hypotenuse = √ ( Adjacent side² + Opposite side²) = √(8²+15²) = √(64+225) = √289 = 17

Sin A = Opposite side/Hypotenuse = 15/17

sec A= Hypotenuse/Adjacent side = 17/8

Answer 2

Answer:

$\large sin \ A=\dfrac{15}{17}\\\\\\\large sec \ A=\dfrac{17}{8}$

Step-by-step explanation:

Given :

15 cot A = 8

We have to find sin A and sec A

We know that

$\large cot \ A=\dfrac{base}{perpendicular}=\dfrac{8}{15}$

Using pythagoras theorem we find hypotenuse

$\large hypotenuse=\sqrt{15^2+8^2}\\\\\\\large hypotenuse=\sqrt{225+64}\\\\\\\large hypotenuse=\sqrt{289}\\\\\\\large hypotenuse=17$

Now we know that for

$\large sin \ A=\dfrac{perpendicular}{hypotenuse}=\dfrac{15}{17}\\\\\\\large sec \ A=\dfrac{hypotenuse}{base}=\dfrac{17}{8}$

Thus we get answer.