The shadow length of Kyle is 1.2 feet,if a lighthouse is 150 feet tall and cast a shadow of 30 feet. Kyle is standing next to a lighthouse and is 6 feet tall.
Step-by-step explanation:
The given is,
A lighthouse is 150 feet tall.
Cast a shadow of 30 feet.
Kyle is 6 feet tall.
Step:1
Ref the attachment,
From triangle ABC,
tan ∅ = [tex]\frac{Opp}{Adj}[/tex]......................(1)
Where, Opp = AB = 150 feet
Adj = BC = 30 feet
Equation (1) becomes,
tan ∅ = [tex]\frac{150}{30}[/tex]
= 5
∅ = [tex]tan^{-1}[/tex] 5
∅ = 78.69°
∅ is same for both ABC and PQR triangle.
From triangle PQR,
tan ∅ = [tex]\frac{Opp}{Adj}[/tex]......................(1)
Where, Opp = PQ = 6 feet
Adj = QR = x
Equation (1) becomes,
tan 78.96° = [tex]\frac{6}{x}[/tex]
5 = [tex]\frac{6}{x}[/tex]
x = [tex]\frac{6}{5}[/tex] = 1.2
Shadow length of Kyle, x = 1.2 feet
Result:
The shadow length of Kyle is 1.2 feet, if a lighthouse is 150 feet tall and cast a shadow of 30 feet. Kyle is standing next to a lighthouse and is 6 feet tall.
