# Determine vertical height of a geometry

• joeldiraviam
In summary: QR is equal to the radius of RS (r). Using this information, we can set up the equation (x - 0)^2 + (y - k)^2 = r^2. We also know that the distance between the centerpoint and ST is equal to the radius of ST (r). Using this information, we can set up the equation (x - 0)^2 + (y - (H1 + r))^2 = r^2. Solving these two equations simultaneously will give us the coordinates of the centerpoint (x,y).In summary, to find the vertical heights of the two arcs (H2 and H3) and the arc centerpoint location, we can use a combination of the Py
joeldiraviam
Hi all,

I have attached a geometry. For this geometry I would like to determine vertical heights of two arcs(H2 and H3).

a) QR is a angle line with known length and angle
b) ST is an arc with known radius. The arc center lies on the whole geometry vertical centerline
c) RS is an arc with known radius. It is tangent to QR line and ST arc.

I need to find H1, H2 and H3. H1 is easy to find but the other two I find it difficult to get the equations. Can someone help me with the answers.

Also is there a way to find the RS arc centerpoint location based on the X and Y locations of the slant line QR. Any help will be greatly useful.

Thanks,
Joel

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• Geom.jpg
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Hi Joel,

Thank you for sharing your geometry and questions with us. I can provide some guidance on how to approach finding the vertical heights of the two arcs (H2 and H3) and the arc centerpoint location.

To find H2 and H3, we can use the Pythagorean theorem and trigonometric functions. Here are the steps:

1. First, we need to find the length of QR. Since we know the length and angle of QR, we can use the trigonometric function cosine (cos) to find the length of the adjacent side (which is QR). The formula is cos(angle) = adjacent/hypotenuse. In this case, cos(Q) = QR/H1. Solving for QR, we get QR = H1 * cos(Q).

2. Next, we can use the Pythagorean theorem to find the length of RS. The formula is c^2 = a^2 + b^2, where c is the hypotenuse (RS), and a and b are the other two sides (QR and ST). Substituting the values we know, we get RS^2 = (H1 * cos(Q))^2 + (H1 + r)^2, where r is the radius of ST. Solving for RS, we get RS = √[(H1 * cos(Q))^2 + (H1 + r)^2].

3. Now, to find H2 and H3, we can use the trigonometric function sine (sin). The formula is sin(angle) = opposite/hypotenuse. In this case, sin(H2 angle) = H1/(H1 + r). Solving for H2, we get H2 = (H1 + r) * sin(H2 angle). Similarly, sin(H3 angle) = (H1 + r)/RS. Solving for H3, we get H3 = RS * sin(H3 angle).

4. To find the arc centerpoint location, we can use the formula for the equation of a circle, which is (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the centerpoint, and r is the radius. In this case, the centerpoint lies on the vertical centerline, so h = 0. We also know that the centerpoint is tangent to the QR line, so the distance between the center

## What is the formula for determining the vertical height of a geometry?

The formula for determining the vertical height of a geometry is vertical height = (distance between base and top) / (cosine of angle of elevation).

## How do I measure the distance between the base and top of a geometry?

The distance between the base and top of a geometry can be measured using a ruler, measuring tape, or other measuring tool.

## What is the angle of elevation?

The angle of elevation is the angle between the horizontal line and the line of sight to the top of the geometry.

## Can I use this formula for any type of geometry?

Yes, this formula can be used for any type of geometry as long as the base and top can be clearly defined and the angle of elevation can be measured.

## Do I need any special tools to determine the vertical height of a geometry?

No, you do not need any special tools to determine the vertical height. However, having a measuring tool and protractor can make the process more accurate.

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