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Ask Your Teacher At a point 55 feet from the base of a church, the angles of elevation to the bottom of the steeple and the top of the steeple are 40° and 47°, respectively. Find the height of the steeple. (Round your answer to one decimal place.)

Respuesta :

Answer:the height of the steeple is 12.8 feet

Step-by-step explanation:

The diagram of the triangle formed is shown in the attached photo.

The triangle formed is triangle ABC and it is a right angle triangle. So angle B is 90 degrees.

Let x represent the height of the steeple.

Let y represent the height from the base of the church to the bottom of the steeple.

Applying trigonometric ratio,

tan # = opposite side / adjacent side

tan 40 = y/55

y = 55tan40

y = 55 × 0.8391 = 46.1505

BC = x + y

tan 47 = BC/55

BC = 55tan47

BC = 55× 1.0724

BC = 58.982

x = BC - y

x = 58.982 - 46.1505

x = 12.8 feet

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