From a point 55 feet in front of a church, the angles of elevation to the base of the steeple and the top of the steeple are 35 degree and 49 degree 20 minutes, respectively, Find the height of the steeple. (Round your answer to one decimal place).
55*(tan49.33 -tan35)
Do the numbers.
mbk,
To find the height of the steeple, we can use trigonometry. Let's call the height of the steeple "h".
First, let's find the distance from the point in front of the church to the base of the steeple. We can use the tangent function to find this distance.
tan(35°) = h / x
Where x is the distance we want to find.
Rearranging the equation, we get:
x = h / tan(35°)
Now, let's find the distance from the point in front of the church to the top of the steeple. We can again use the tangent function:
tan(49°20') = h / (x + 55)
Where (x + 55) is the total distance from the point to the top of the steeple.
Rearranging the equation, we get:
(x + 55) = h / tan(49°20')
Now, we can substitute the expression for x from the first equation into the second equation to eliminate x:
(h / tan(35°)) + 55 = h / tan(49°20')
Now, let's solve this equation for h.
Multiply both sides of the equation by tan(35°) * tan(49°20'):
tan(49°20') * h + 55 * tan(49°20') = tan(35°) * h
Subtract tan(35°) * h from both sides:
tan(49°20') * h - tan(35°) * h = -55 * tan(49°20')
Factor out h:
h * (tan(49°20') - tan(35°)) = -55 * tan(49°20')
Divide both sides by (tan(49°20') - tan(35°)):
h = (-55 * tan(49°20')) / (tan(49°20') - tan(35°))
Using a scientific calculator, we find:
h ≈ 64.1 feet
Therefore, the height of the steeple is approximately 64.1 feet.
To find the height of the steeple, we can use trigonometry and create a right triangle.
Let's label the points:
- Point A: the point 55 feet in front of the church.
- Point B: the base of the steeple.
- Point C: the top of the steeple.
We are given two angles of elevation:
- Angle of elevation from Point A to Point B: 35 degrees.
- Angle of elevation from Point A to Point C: 49 degrees 20 minutes.
Now, we can set up some trigonometric ratios.
First, let's consider the triangle formed by Point A, Point B, and the height of the steeple (unknown). We'll call this unknown height "h".
Using the tangent function, we have:
tan(35 degrees) = h / 55
Rearranging the equation, we get:
h = 55 * tan(35 degrees)
Next, let's consider the triangle formed by Point A, Point C, and the height of the steeple (unknown). We'll again call this unknown height "h".
Using the tangent function, we have:
tan(49 degrees 20 minutes) = h / 55
To use the tangent function, we need to convert the angle from degrees and minutes to decimal degrees. There are 60 minutes in a degree, so 20 minutes is equal to 20/60 = 1/3 degree. Therefore:
tan(49 degrees 20 minutes) = tan(49.333 degrees)
Now, we can rearrange the equation to solve for h:
h = 55 * tan(49.333 degrees)
After calculating these two equations, we find that h is approximately equal to 64.6 feet. Therefore, the height of the steeple is approximately 64.6 feet.