Ladders can be extremely dangerous if not used correctly. a 20 ft. extension ladder is played on a wall making and angle 85° with the ground. if a person at top of the ladder leaned back, rotating the ladder away from the wall, how far to the nearest foot would the person fall before he hit the ground?

The person falls a distance of approximately 19.924 feet.

In this question, we must determine the vertical distance travelled by the person (), in feet. Let consider that the ladder is set between a horizontal ground and a vertical wall.

Then, the vertical distance is determined by the following trigonometric expression:

(1)

Where:

If we know that and , then the vertical distance travalled by the person:

The person falls a distance of approximately 19.924 feet.

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Approximately 33 feet

Step-by-step explanation: Please refer to the attched diagram.

The 20ft ladder is placed on the wall at an agle of 85° with the ground.

If the person on the ladder were to lean back and fall to the ground (rotating the ladder away from the wall), then the distance he would have covered before he hits the ground is depicted by the arc as shown in the diagram. The ladder upon touching the ground would remain the same, which is 20 feet. So what the question requires is the length of the arc made during the fall, and the length of the ladder both on the wall an on the floor would be the radius (20 ft) while the angle subtended by the arc is 95° ( angles on a straight line equals 180, that is 85 + 95 = 180)

Therefore the length of an arc is given as;

Length of arc = (∅/360) x 2πr

Where ∅ = 95 and r = 95

Length of arc = (95/360) x 2 x 3.14 x 20

Length of arc = (19/72) x 125.6

Length of arc = 2386.4/72

Length of arc = 33.1444

Length of arc ≈ 33 feet (To the nearest foot)

The person on the ladder would have travelled approximately 33 feet before he/she hits the ground.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

savings account is an account only used for saving money. this acts as an emergency source of funding for an individual. answer a would result in the money in his account to grow as it specifically states that interest is compounded daily at the rate of 2%

step-by-step explanation: