Question

Jake wants the profile of a hotel he is planning to be a right triangle with the dimensions shown. The city prohibits structures over 100 ft at the location where he would like to build. Can the hotel be located there? Explain

Answer 1

The height of the building is 96 ft., hence the building can be located there.

Sine rule

Sine rule is used to show the relationship between the sides and angles of a triangle it is given by:

a / sin(A) = b / sin(B) = c / sin(C)

A, B, C are the angles and a, b, c are the sides opposite the respective angles.

Let A represent the angle opposite side 120 ft., hence:

120/sin(A) = 200/sin(90)

A = 36.9°

Let h represent the height of the building, hence:

h / sin(36.9) = 160 / sin(90)

h = 96 feet

The height of the building is 96 ft., hence the building can be located there.

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