Abridge over a gorge is supported by an arch in the shape of a semi-ellipse. the length of the bridge is 400 ft. and the maximum height is 100 ft. draw a picture of the problem and label it with numeric values. find the height of the arch 50 ft. from the center. round to the nearest foot.

The height of the arch 50ft from the center is 97ft

Step-by-step explanation:

A bridge over a gorge is supported by an arch in the shape of a semi-ellipse

The length of the bridge is 400 ft. and the maximum height is 100 ft

so, a=200ft

b=100ft

(a)

we can draw picture

(b)

now, we can use equation of ellipse formula

now, we can plug

a=200

b=100

we can plug x=50 and find y

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.