Cesar is building a shelf at an angle so that it appears to be leaning against the wall. the shelf touches the wall 7 ft. above the floor and the distance between the floor from the wall to the front of the shelf is 1.5 ft. what is the angle the shelf makes with the floor? a. 77.9 degrees. b. 77.6 degrees. c. 12.1 degrees. d. 12.4 degrees. a 15-ft. building casts a shadow of 12 ft. what is the approximate angle of inclination of the sun? a. 51.3 degrees. b. 53.1 degrees. c. 36.9 degrees. d. 19.2 degrees.

1) The angle the shelf makes with the floor is approximately 77.905°. (Choice A)

2) The approximate angle of inclination of the sun is approximately 51.340°. (Choice A)

1) In this case we know that shelf has a vertical height () of 7 feet and a horizontal distance between the floor from the wall to the front of the shelf () is 1.5 feet. The angle (), in degrees, is determined by tangent function:

The angle the shelf makes with the floor is approximately 77.905°. (Choice A)

2) The length of the shadow () is 12 feet and the height of the building () is 15 feet. The angle of inclination of the sun is determined by tangent function:

The approximate angle of inclination of the sun is approximately 51.340°. (Choice A)

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mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

1. 3. can also be expressed as (22/7)

2. -4.5

3. 3.6

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