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A person at ground level finds the angle of elevation to the top of a building is 40°. After
moving 50 feet further away from the building, the angle of elevation is 32°. What is the height of the building?

Respuesta :

Answer:the height of the building is 122.4 feet.

Step-by-step explanation:

The diagram illustrating the scenario is shown in the attached photo.

Triangle ABC and DBC are right angle triangles.

h represents the height of the building.

Considering triangle ABC,

Tan θ = opposite side/adjacent side

Tan 32 = h/x

h = xtan32 = x × 0.6249

h = 0.6249x - - - - - - - - - - -1

Considering triangle DBC,

Tan θ = opposite side/adjacent side

Tan 40 = h/(x - 50)

h = tan 40(x - 50) = 0.8391(x - 50)

h = 0.8391x - 41.955- - - - - - - - - -2

Equating equation 1 and equation 2, it becomes

0.6249x = 0.8391x - 41.955

0.8391x - 0.6249x = 41.955

0.2142x = 41.955

x = 41.955/0.2142 = 195.87

Substituting x = 195.87 into equation 1, it becomes

h = 0.6249 × 195.87

h = 122.4

Ver imagen Favouredlyf
titanfist345

Answer:122.4

Step-by-step explanation:

Answer:the height of the building is 122.4 feet.

Step-by-step explanation:

The diagram illustrating the scenario is shown in the attached photo.

Triangle ABC and DBC are right angle triangles.

h represents the height of the building.

Considering triangle ABC,

Tan θ = opposite side/adjacent side

Tan 32 = h/x

h = xtan32 = x × 0.6249

h = 0.6249x - - - - - - - - - - -1

Considering triangle DBC,

Tan θ = opposite side/adjacent side

Tan 40 = h/(x - 50)

h = tan 40(x - 50) = 0.8391(x - 50)

h = 0.8391x - 41.955- - - - - - - - - -2

Equating equation 1 and equation 2, it becomes

0.6249x = 0.8391x - 41.955

0.8391x - 0.6249x = 41.955

0.2142x = 41.955

x = 41.955/0.2142 = 195.87

Substituting x = 195.87 into equation 1, it becomes

h = 0.6249 × 195.87

h = 122.4

Read more on Brainly.com - https://brainly.com/question/14793207#readmore

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