Question

write the ratios of cos thita and tan thita from the figute

Answer 1

From the properties of trigonometry, we know :

tane is the ratio of length of perpendicular height for the given angle to the length of base on which angle lies.

And,
cose is the ratio of length of base on which angle lies to the length of hypotenuse.[ the line in front of 90° ( in the question, it is PR ) ].



In the question,
Given angle is $\theta$


Height for $\theta$ is PQ and base is RQ.



Hence,
tan$\theta=\dfrac{PQ}{RQ}$


And,
cos$\theta=\dfrac{RQ}{PR}$



Therefore,
• tan$\theta$= PQ / RQ
• cos$\theta$ = RQ / PR

Answer 2

Here theta represent an angle

I will use A in place of theta
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From Formula
Cos A=Base/Hypotenuse
Tan A=Perpendicular/Base
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From figure:-
Perpendicular=PQ
Base=QR
Hypotenuse=PR
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Hence,
→Cos A=QR/PR
→Tan A=PQ/QR