Two buildings are 30 ft apart. The angle of elevation from the top of one to the top of the other is 19°. What is their difference in height?
After you make a sketch and let the additional height be h, it should be clear that
tan 19° = h/30
h = 30tan19 = appr 10.3 ft
Well, I have to say, these two buildings really know how to keep their distance! But let's help you out with some math.
To find the difference in height, we can use a bit of trigonometry. Since we have the angle of elevation, we can use the tangent function.
Tangent(angle of elevation) = height difference / distance between buildings
So, we can rearrange the equation to solve for the height difference:
Height difference = Tangent(angle of elevation) * distance between buildings
Plugging in the values, we get:
Height difference = Tangent(19°) * 30 ft
And I could give you the numerical answer, but where's the fun in that? Let's just say that the buildings have a "height differential" that would give even the most talented acrobats a run for their money!
To find the difference in height between the two buildings, we can use trigonometry. Let's denote the height of the first building as h1 and the height of the second building as h2.
We are given that the two buildings are 30 ft apart. The angle of elevation from the top of one building to the top of the other is 19°.
Using trigonometry, we can set up the following equation:
tan(19°) = (h2 - h1) / 30
To solve for h2 - h1, we can rearrange the equation:
h2 - h1 = 30 * tan(19°)
Using a calculator, we can evaluate the right side of the equation:
h2 - h1 = 30 * 0.334
h2 - h1 ≈ 10.02
Therefore, the difference in height between the two buildings is approximately 10.02 feet.
To find the difference in height between the two buildings, we can use trigonometry.
Let's assign variables to the given information:
- Let A be the height of the first building.
- Let B be the height of the second building.
- Let C be the distance between the two buildings.
Now, let's draw a diagram to visualize the problem:
A
/|
/ | C
/ |
/ |
/ |
/ |
/ θ |
/______|
B
From the diagram, we can see that tan(θ) = (A - B) / C.
Since the angle of elevation is given as 19°, we can write this equation as:
tan(19°) = (A - B) / 30.
Now, let's solve this equation for the difference in height (A - B):
A - B = tan(19°) * 30.
Using a scientific calculator, we can find that tan(19°) is approximately 0.3420.
Now, we can substitute this value back into the equation:
A - B = 0.3420 * 30.
Calculating this expression, we find:
A - B = 10.26 ft.
Therefore, the difference in height between the two buildings is approximately 10.26 ft.