A drawbridge is 150 feet long when stretched across The two

A drawbridge is 150 feet long when stretched across. The two sections of the bridge can be rotated upward through an angle of 35. a if the water level is 15 feet below the closed bridge, find the distance,d, between the end of section and the water level when the bridge is fully open

B- Approximately how far apart are the ends of the two sections when the bridge if fully opened?

Solution

(a)

we are given that

we know that each half of the 150-feet span forms a right triangle when itwill be opened

And one side is the height above its closed position and the hypotenuse is the 75 feet length of the section

we know that angle of rotation or A =35 degree
so, we can apply sine formula to \'d\'
sin(35) = oppsosite /hyp

sin(35)=h/75

h=75*sin(35)

d=43.018 feet

for finding the height over the river, we need to add the 15 feet that the bridge is above the river

so,  distance,d, between the end of section and the water level when the bridge is fully open = 43.018+15=58.0182

so,  distance,d, between the end of section and the water level when the bridge is fully open is 58.0182 feet......Answer

(b)

we know that for finding the distance between the two ends

we have to look at the two right triangles formed between the bridge segments and the endpoints of the bridge

we know that the bridge is raised to 35 degrees

And the angle between a vertical line drawn through the endpoint of the bridge and the bridge section is 90 - 35=55 degrees.

we also know that hypotenuse is 75-feet bridge section

now, we will use the sine function due to the distance is opposite the 55 degree angle

so, we get

sin(55)=d/75

d=75*sin(55)

d=61.436feet

It means that each section sticks out 61.436 feet from the end of the bridge to which it\'s attached

and we know that each side sticks out equally

so, the gap between the two ends is twice that value subtracted from the total span

gap is

150 - (2 * 61.436)

gap is 27.128 feet ..........Answer