Question

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. how long is his shadow?

Answer 1

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.

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 ∅ =
`(Opp)/(Adj)`......................(1)

Where, Opp = AB = 150 feet

Adj = BC = 30 feet

Equation (1) becomes,

tan ∅ =
`(150)/(30)`

= 5

∅ =
`tan^(-1)` 5

∅ = 78.69°

∅ is same for both ABC and PQR triangle.

From triangle PQR,

tan ∅ =
`(Opp)/(Adj)`......................(1)

Where, Opp = PQ = 6 feet

Adj = QR = x

Equation (1) becomes,

tan 78.96° =
`(6)/(x)`

5 =
`(6)/(x)`

x =
`(6)/(5)` = 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.