Well, not being a surveyor, I'm a little uncertain about how to picture the angles but I am going to assume the following:

"E 84 degrees N from the left marker" means that if you are located directly at the left marker and looking east, then a sweep angle of 84 degrees towards the north would align your view to the boulder; conversely, "W 76 degrees N from the right marker" means that if you are located at the right marker and looking west, then a sweep angle of 76 degrees towards the north would align your view to the boulder

this becomes a simple trig problem of right triangles since the surveyor is perpendicular to the boulder after walking a straight line between the two markers for 11.22 yards; we also assume that all measurements are taken within the same altitude plane

the three sides, "marker right"-boulder-"current position", form a right triangle with a base leg of 11.22 yards whose other leg represents the distance across the river

let 'x' represent the distance across the river, then we have:

tan(76-degrees) = x/11.22

x = 11.22 * tan(76) = 45

the distance across the river is 45 yards, and we find the distance between the markers by solving a right triangle whose sides are "the distance from the surveyor to the left marker", "the distance across the river" [now known] and "the distance from the right marker to the boulder":

let 'x' now represent the distance from the left marker to the surveyor, then:

tan(84) = 45/x

x = 45/(tan(84)) = 4.729

11.22 + 4.729 = 15.95

the distance across the river is approximately 45 yards, the distance between the two markers is approximately 16 yards