An escalator 152 feet in length rises to a platform and makes a 31° angle with the ground. Find the height of the platform above the ground.

78.3 or 78.29

Step-by-step explanation:

We are asked to find the height of the figure which is the vertical side of the triangle. We are given an angle and we are a side opposite of that angle( the height of the platform) and the hypotenuse 152. So we are going to use sine.

Opposite/Hypotenuse

We use this equation

Plug in the values

Which is about 78.29

c. 0.1391 < Ï < 0.2311

Step-by-step explanation:

The formula for Confidence Interval is given as:

Mean ± z × Standard deviation/√n

Z score for 98% confidence interval = 2.326

Mean = Significance level = 100% - 98%

= 2% = 0.02

Standard deviation = S=0.0165

n= 37

Hence,

Confidence Interval =

0.02 ± 2.326 × 0.0165/√37

0.02 ± 0.0063094687

Confidence Interval

0.02 - 0.0063094687

= 0.1391

0.02 ± 0.0063094687

= 0.2311

Hence, the Confidence Interval = (0.1391, 0.2311)

= c. 0.1391 < Ï < 0.2311