## The arm of a steel crane is 62 feet long. When it is fully extended, the crane arm forms a 30 degree angle with a line parallel to the groun

Question

The arm of a steel crane is 62 feet long. When it is fully extended, the crane arm forms a 30 degree angle with a line parallel to the ground. How many feet above the ground is the top of the crane?

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3 weeks 2021-09-08T11:56:47+00:00 2 Answers 0

1. Answer: The top of the Crane is 31 feet above the ground.

Step-by-step explanation:

When it is fully extended, the crane arm forms a 30 degree angle with a line parallel to the ground. This means that a right angle triangle is formed. The length of the Crane’s arm represents the hypotenuse. The horizontal distance represents the adjacent side of the right angle triangle. The distance, h of the top of the Crane from the ground represents the opposite side of the right angle triangle.

To determine h, we would apply

the Sine trigonometric ratio.

Sin θ, = opposite side/hypotenuse. Therefore,

Sin 30 = h/62

h = 62Sin30

h = 62 × 0.5

h = 31 feet

38

Step-by-step explanation:

Sin 30 = h/62

h = 62Sin30

h = 62 × 0.5

h = 31 feet

h=31+7 (because it is already off the floor)

h=38