Answer :
Say theta=β for the sake of this problem. There isn't a theta sign I can use on Brainly.
cosβ=A/H=3/5
So the adjacent side of the right angled triangle is 3 and the hypotenuse of the right angled triangle is 5. Let's find its opposite side as tanβ=(sinβ)/(cosβ) and sinβ=O/H.
3²+Opposite²=5²
9+Opposite²=25
Opposite²=25-9
Opposite²=16
Opposite=√16=4
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With this knowledge we can say that:
sinβ=O/H=4/5
Therefore:
tanβ=(4/5)/(3/5)
=(4/5) * (5/3)
=20/15
=4/3
-------------------------
tanβ=4/3
cosβ=A/H=3/5
So the adjacent side of the right angled triangle is 3 and the hypotenuse of the right angled triangle is 5. Let's find its opposite side as tanβ=(sinβ)/(cosβ) and sinβ=O/H.
3²+Opposite²=5²
9+Opposite²=25
Opposite²=25-9
Opposite²=16
Opposite=√16=4
---------------------------
With this knowledge we can say that:
sinβ=O/H=4/5
Therefore:
tanβ=(4/5)/(3/5)
=(4/5) * (5/3)
=20/15
=4/3
-------------------------
tanβ=4/3
