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.)
1 answer:
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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