Answer:
Option (2) and Option (4)
Step-by-step explanation:
From the picture attached,
Length of ladder AC = 20 feet
Height of the highest point of the ladder from ground AB = 16 ft
By Pythagoras theorem,
AC² = BC² + AB²
BC² = AC² - AB²
BC = [tex]\sqrt{(20)^2-(16)^2}[/tex]
= [tex]\sqrt{400-256}[/tex]
= [tex]\sqrt{144}[/tex]
= 12
Now, Sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}=\frac{\text{AB}}{\text{AC}}[/tex]
= [tex]\frac{16}{20}[/tex]
Cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{\text{BC}}{\text{AC}}[/tex]
= [tex]\frac{12}{20}[/tex]
tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{\text{AB}}{\text{BC}}[/tex]
= [tex]\frac{16}{12}[/tex]
Therefore, Option (2) and Option (4) are the correct options.
The equation that should be used is option 2 and option 4.
Since
Length of ladder AC = 20 feet
Height of the highest point of the ladder from ground AB = 16 ft
So here we apply the Pythagoras theorem,
AC² = BC² + AB²
BC² = AC² - AB²
So,
[tex]BC = \sqrt{(20)^2 - (16)^22}\\\\ = \sqrt{400 - 256}\\\\ = \sqrt{144}[/tex]
= 12
Now
Sin θ = 16\20
Cos θ = 12\20
tan θ = 16 \12
hence, The equation that should be used is option 2 and option 4.
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