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Lynna [10]
3 years ago
12

Frank stands 500 feet from the base of the Statue of Liberty. If Frank looks up with an angle of elevation of 30', how tall is t

he Statue of Liberty, to the nearest foot?
Mathematics
1 answer:
Over [174]3 years ago
4 0
Answer: 289 ft.

Explanation:

You can form a right triangle with these features:

1) Base = adjacent-leg = 500 feet

2) angle between the hypotenuse and the base = 30° ( I use 30° instead of 30', because 30' does not make sense, it is a too small angle)

3) Height = opposite-leg = height of the Statue of LIberty = x

Now, use the equation for the trigonometric ratio tangent:

tan(angle) = opposite-leg / adjacent-leg

=> tan (30°) = x / 500ft

=> x = 500ft * tan(30°)

x = 288.67 ft which rounded to the nearest foot is 289 ft.
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What is a positive angle less than 360 degrees that is conterminal with -289 degrees
wel

Answer:

The positive angle that less than 360° and is conterminal with -289° is 71°

Step-by-step explanation:

  • When a terminal of an angle moves anticlockwise, then it makes a positive angle with the positive part of the x-axis
  • When a terminal of an angle moves clockwise, then it makes a negative angle with the positive part of the x-axis
  • To find the positive angle which has the same terminal of a negative angle add the measure of the negative angle by 360°

Let us solve the question

∵ The measure of the angle is -289°

→ Add its measure by 360° to find the positive angle that is conterminal

   with it

∵ The measure of the positive angle = -289° + 360°

∴ The measure of the positive angle = 71°

The positive angle that less than 360° and is conterminal with -289° is 71°

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