A ramp 23ft long rises to a platform. The bottom of the platform is 11ft from the foot of the ramp. Find x, the angle of elevation of the ramp. Round your answer to the nearest tenth of a degree.

61.4°

Step-by-step explanation

Given

Length of the ramp = 23ft = hypotenuse

Base of the ramp = 11ft = Adjacent

Required

Angle of elevation x

Using the SOH CAH TOA identity

Cos theta =adj/hyp

Cos x = 11/23

Cos x = 0.4782

x = arccos0.4782

x = 61.42°

Hence the angle of elevation is 61.4°

You can convert the denominator of each to 16 to compare each fraction. The wrenches should go in order from least to greatest: 5/16, 3/8, 7/16, 1/2, 9/16, 5/8, 11/16, and 3/4. Place on number line between 0 and 1. The number line shows values that are least on the left to the greatest values to the right.

Step-by-step explanation:

You can find a common denominator to compare all the fractions. The common denominator should be the LCM or lowest common multiple of 2, 4, 8, and 16. Since all can multiply to 16, this is the common denominator.

1/2 = 8/16

3/4 = 12/16

3/8 = 6/16

5/8 = 10/16

5/16

7/16

9/16

11/16

Now place in order according to the numerator value:

5/16, 6/16, 7/16, 8/16, 9/16, 10/16, 11/16, and 12/16. We'll now write the list using the original fractions instead of their conversions.

5/16, 3/8, 7/16, 1/2, 9/16, 5/8, 11/16, and 3/4

Place these on the number line in order between 0 and 1.