A tower that is 65m high makes an obtuse angle with the ground. The vertical distance from the top of the tower to the ground is 59m. What obtuse angle does the tower make with the ground?
To find the obtuse angle that the tower makes with the ground, we can use trigonometry and the given information.
Let's denote the obtuse angle as θ.
Using basic trigonometric ratios, we know that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is the vertical distance from the top of the tower to the ground (59m), and the adjacent side is the height of the tower (65m).
Therefore, we can write the equation:
tan(θ) = opposite/adjacent
tan(θ) = 59/65
Now, to find the value of θ, we need to use the inverse tangent function (also known as arctan or tan^(-1)).
θ = arctan(59/65)
Using a scientific calculator, we can find the inverse tangent of 59/65:
θ ≈ 42.29 degrees
So, the obtuse angle that the tower makes with the ground is approximately 42.29 degrees.
To find the obtuse angle that the tower makes with the ground, we can use trigonometry. Specifically, we can use the inverse tangent function.
Let's denote the height of the tower as h = 65m and the vertical distance from the top of the tower to the ground as a = 59m. The angle we want to find is the angle formed between the ground and a line connecting the top of the tower to the ground.
Using the formula for the tangent of an angle:
tan(angle) = opposite / adjacent
In this case, the opposite side is h = 65m and the adjacent side is a = 59m. So we have:
tan(angle) = h / a
Substituting the given values, we get:
tan(angle) = 65 / 59
Now we can take the inverse tangent of both sides to find the angle:
angle = arctan(65 / 59)
Using a calculator, we find that:
angle ≈ 48.97 degrees
Therefore, the obtuse angle that the tower makes with the ground is approximately 48.97 degrees.
I am visualizing something like the Leaning Tower of Pisa.
The statement "A tower is 65 m high" is misleading, since height is measured along a perpendicular.
In the next sentence you say "the vertical distance from the top of the tower to the ground is 59 m"
Thus I will assume that the "length" of the tower is 65 m.
So in effect you have a right angled triangle with hypotenuse 65, and opposite side 59
let the angle at the base be Ø
sinØ = 59/65 = .90769...
Ø = 65.2° making the obtuse angle 114.8°