A life guard is sitting on a platform, looking down at a swimmer in the water. If the lifeguards line of sight is 8 feet above the ground and the angle of depression is 18 degrees, how far away is the swimmer from the lifeguard? Round to the nearest tenth

The swimmer is 26 ft (approximately) away from the lifeguard

Step-by-step explanation: Please refer you the attached diagram.

The lifeguard sitting on the platform is labeled as point P, and the swimmer down below is at point S. The point G is the point directly beneath the lifeguard. So, we have a right angled triangle PSG. Also the angle of depression is 18 degrees, so the angle of sight between the lifeguard and the ground is 72 degrees (that is, 90 - 18 = 72).

Having derived a right angled triangle with two sides and a reference angle, we can now use the trigonometric ratio which is;

CosP = Adjacent/Hypotenuse

The adjacent is the side that lies between the reference angle and the right angle (side PG), while the hypotenuse is the side facing the right angle (side PS). Hence;

Cos72 = 8/g

By cross multiplication we now have

g = 8/Cos72

g = 8/0.3090

g = 25.8899

Approximately, g = 26 ft.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed