# A bridge

A bridge over a river has the shape of the arc with bases of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. How wide is the river?

### Correct answer:

**Showing 2 comments:**

**Dr Math**

r = radius of circle of arc

x = distance between center of circle and water level (center of the circle is under ground)

y = distance in horiznotal of point on circle which is 9 ft above the water

x = distance between center of circle and water level (center of the circle is under ground)

y = distance in horiznotal of point on circle which is 9 ft above the water

Tips to related online calculators

Looking for help with calculating roots of a quadratic equation?

Do you have a system of equations and looking for calculator system of linear equations?

Pythagorean theorem is the base for the right triangle calculator.

See also our trigonometric triangle calculator.

Do you have a system of equations and looking for calculator system of linear equations?

Pythagorean theorem is the base for the right triangle calculator.

See also our trigonometric triangle calculator.

#### You need to know the following knowledge to solve this word math problem:

## Related math problems and questions:

- Bamboo

Bamboo high 32 feet was at a certain height broken by the wind so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken? - Arc

Calculate span of the arc, which is part of a circle with diameter d = 20 m and its height is 6 m. - The bridge

A vehicle weighing 5,800 kg passes 41 km/h on an arched bridge with a radius of curvature of 62 m. What force is pushing the car onto the bridge as it passes through the center? What is the maximum speed it can cross over the center of the bridge so that - Quarter circle

What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm? - Track arc

Two straight tracks is in an angle 74°. They will join with circular arc with radius r=1127 m. How long will be arc connecting these lines (L)? How far is the center point of arc from track crossings (x)? - Arc and segment

Calculate the length of circular arc l, area of the circular arc S_{1}and area of circular segment S_{2}. Radius of the circle is 11 and corresponding angle is ?. - Bridge

The bridge arc has a span 34 m and height 3 m. Calculate the radius of the circle arc of this bridge. - Circle chord

Calculate the length of the chord of the circle with radius r = 10 cm, length of which is equal to the distance from the center of the circle. - MO SK/CZ Z9–I–3

John had the ball that rolled into the pool, and it swam in the water. Its highest point was 2 cm above the surface. The diameter of the circle that marked the water level on the surface of the ball was 8 cm. Find the diameter of John ball. - Circle

The circle touches two parallel lines p and q, and its center lies on line a, which is the secant of lines p and q. Write the equation of the circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0 - Trapezoid

trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area? - Circle and square

An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD. - Chord

In a circle with radius r=60 cm is chord 4× longer than its distance from the center. What is the length of the chord? - Equation of circle

find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16. - Two chords

Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle. - Find parameters

Find parameters of the circle in the plane - coordinates of center and radius: ? - Find the 5

Find the equation of the circle with center at (1,20), which touches the line 8x+5y-19=0