John is looking at the top of a building and thinking it would be great to make a zipline from the top to your current location. He measures the angle of elevation as 28° and is 182 feet from the base of the building. How long a zipline is needed if John is 71.5 inches tall? Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the answer rounded to the nearest tenth of a foot.

60

step-by-step explanation:

every triangle measures a total of 120 degrees. you have to find angle c. we know that isosceles triangles angles are equal. 60 degrees plus 60 degrees gives you 120.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places

6 and 24

step-by-step explanation:

6 x 4 = 24

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