Answer:
x = 9.6 meters
y = 20.98 meters
Shadow length = 11.38 meters
Step-by-step explanation:
By applying tangent rule in right triangle ABD,
tan(21)° = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(21) = [tex]\frac{x}{25}[/tex]
x = 25(tan 21)
x = 9.5966
x ≈ 9.60 meters
Similarly, by applying tangent rule in ΔABC,
tan(40)° = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(40)° = [tex]\frac{BC}{AB}[/tex]
tan(40)° = [tex]\frac{y}{25}[/tex]
y = 25(tan 40°)
y = 20.98 meters
Length of the shadow of the man = y - x
= 20.98 - 9.60
= 11.38 meters
