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.

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 ∅ = $\frac{Opp}{Adj}$......................(1)

                 Where, Opp = AB = 150 feet

                                Adj = BC = 30 feet

                 Equation (1) becomes,

                              tan ∅ = $\frac{150}{30}$

                                        = 5

                                     ∅ = $tan^{-1}$ 5

                                     ∅ = 78.69°

                 ∅ is same for both ABC and PQR triangle.

                 From triangle PQR,

                               tan ∅ = $\frac{Opp}{Adj}$......................(1)

                 Where, Opp = PQ = 6 feet

                                Adj = QR = x

                 Equation (1) becomes,

                      tan 78.96° = $\frac{6}{x}$

                                     5 = $\frac{6}{x}$

                                     x = $\frac{6}{5}$ = 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.