The angle of elevation of the top of a tower to point A on the ground is 61 degrees. At point B it is 600 feet farther from the base, in line with the base and the first point and in the same plane, the angle of elevation is 32 degrees. Find the height of the tower.
This problem is tricky because I don't know the distance point A is from the base. Point B would be a distance of 600ft.+ the distance of point A, I think.
A 200 ft guy wire is attached to the top of a tower.If the wire makes a 55 grados angle with the ground, how tall is the tower?
32
To solve this problem, we can use trigonometry and set up two right triangles. Let's label the height of the tower as "h", the distance from the base to point A as "d", and the distance from the base to point B as "d + 600".
First, we'll consider the triangle formed between the tower's height, point A, and the base of the tower. In this triangle, the angle of elevation from point A is 61 degrees.
Using the tangent function, we can write the equation:
tan(61) = h / d
Next, we'll consider the triangle formed between the tower's height, point B, and the base of the tower. In this triangle, the angle of elevation from point B is 32 degrees.
Again using the tangent function, we can write the equation:
tan(32) = h / (d + 600)
Now we have a system of two equations with two variables (h and d). We can solve this system to find the height of the tower.
To eliminate the variable "h", divide the two equations:
(tan(61))/(tan(32)) = (h/d) / (h/(d + 600))
Simplifying, we have:
tan(61) / tan(32) = d / (d + 600)
Now, we can solve this equation to find the value of "d".
tan(61) / tan(32) = d / (d + 600)
Using a scientific calculator, find the tangent of 61 degrees and divide it by the tangent of 32 degrees. Round this value to the nearest hundredth.
Next, cross multiply and solve for "d":
(tan(61) / tan(32))(d + 600) = d
Multiply the value of (tan(61) / tan(32)) by (d + 600), and then distribute this value:
(tan(61)/tan(32)) * d + (tan(61)/tan(32)) * 600 = d
Subtract d from both sides of the equation:
(tan(61)/tan(32)) * d - d = - (tan(61)/tan(32)) * 600
Factor out "d" from the left side of the equation:
d * ((tan(61)/tan(32)) - 1) = - (tan(61)/tan(32)) * 600
Now, divide both sides of the equation by ((tan(61)/tan(32)) - 1) to solve for "d":
d = - (tan(61)/tan(32)) * 600 / ((tan(61)/tan(32)) - 1)
Using a scientific calculator, evaluate the right side of the equation. Round this value to the nearest hundredth.
Once we find the value of "d", we can substitute it back into either of the original equations to find the value of "h".
h = (tan(61)/tan(32)) * d
Using a scientific calculator, evaluate the right side of the equation, using the value of "d" previously found. Round this value to the nearest hundredth.
The resulting value is the height of the tower.
heigth=A*tan61
height=B*tan32
where A and B are the distances from the tower. B-A=600 or B=600+A
subtract equation 2 from 1
height-height=0=Atan61-(600+A)tan32
solve for A
then, solve for height.