Answer:
tan∠A = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
SOHCAHTOA
O= Opposite
H= Hypotenuse
A = Adjacent
So according to this the 3 is the opposite side and 5 is the hypotenuse.
So we need to find adjacent side for Tan.
For this we will use pythagorean theorem. [tex]a^{2} + b^{2} = c^{2}[/tex] c is the hypotenuse, b is the base.
We are sure that the hypotenuse is 5 but we dont know which side is 3 but it wont matter we can put it in either a or b because it would be adjacent at the end as we already know the other 2.
[tex]3^{2} +b^{2} = 5^{2} \\9 + b^{2} = 25\\b^{2} = 16\\b^{2} = 4^{2} \\b = 4[/tex]
So the adjacent side 4. Now according to TOA tan∠A = [tex]\frac{3}{4}[/tex]
