Question

A street with two lanes, each 10 ft wide, goes through a semicircular tunnel
with radius 12 ft. How high is the tunnel at the edge of each lane?​

Answer 1

Answer:

The equation of the tunnel is x^2 + y^2 = 81

The height at each side is the y-value of the intersection of the circle and x = 5.

x^2 + y^2 = 81

25 + y^2 = 81

y^2 = 56

y = sqrt(56) =~ Ans 7.48 feet

Answer 2

Answer:

7.48 feet

Step-by-step explanation:

Semicircular tunnel means a half of a circle in shape of the tunnel. That was very close to the two lanes with radius related to the semicircular tunnel.

Given that:

Street with two lanes = 10ft

Radius of semicircular tunnel = 12 ft

To find:

The height of tunnel at edge of each lane =?

Solution:

Let the equation of tunnel be

$x^2 + y^2 = 81$

let the height of each sides be the value of y with an intersection of circle.

Then, x=5

$x^2 + y^2 = 81$

$25 + y^2 = 81$

$y^2 = 56$

= 7.48 feet

Therefore, the height of the tunnel is 7.48 feet

#SPJ3