SOLUTION: from a point 50 feet in front ofrom a point 50 feet in front of a church, the angles of elevation to the base of the steeple and the top of the steeple are 35 degrees adn 47 degree

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Question 420154: from a point 50 feet in front ofrom a point 50 feet in front of a church, the angles of elevation to the base of the steeple and the top of the steeple are 35 degrees adn 47 degrees respectively. find the height of the steeple.f a church, the angles of elevation to the base of the steeple and the top of the steeple are 35 degrees and 47 degrees respectively. find the height of the steeple.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
you know the angle and you know the length of the adjacent side.

you can find the length of the opposite side by using the tangent formula.

let A be the point 50 feet from the side of the church.

let B be the point at the base of the church.

let C be the point at the base of the steeple.

let D be the point at the top of the steeple.

the 35 degree angle forms the triangle ABC which takes you from the base of the church to the base of the steeple.

the 47 degree angle forms the triangle ABD which takes you from the base of the church to the top of the steeple.

tangent of 35 degrees equals BC / AB

tangent of 47 degrees equals BD / AB

AB = 50, so the equations become:

tangent of 35 degrees equals BC / 50

tangent of 47 degrees equals BD / 50

multiply both sides of each equation by 50 to get:

tangent of 35 degrees times 50 equals BC

tangent of 47 degrees times 50 equals BD.

use your calculator to find the tangenst to get:

.700207538 * 50 = BC.

1.07236871 * 50 = BD.

simplify to get:

35.01037691 = BC

53.6184355 = BD

the height of the steeple is equal to BD minus BC which equals 53.6184355 - 35.01037691 which equals 18.60805859 feet.

the height of the steeple is equal to 18.6 feet rounded to the nearest 10th of a foot.

a picture of the triangles created is shown below: