ANGLES IN STANDARD POSITION PRACTICAL PROBLEMS

Problem 1 :

A 10-m boom lifts material onto a roof in need of repair. Determine the exact vertical displacement of the end of the boom when the operator lowers it from 60° to 30°.

Solution :

sin 60  =  V₁/10

√3/2  =  V₁/10

V₁  = 10√3/2 = 5√3

sin 30  =  V₂/10

1/2  =  V₂/10

V₂  =  10/2 = 5

V₁ - V₂  =  5√3 - 5

=  5(√3 - 1) m

Problem 2 :

Engineers use a bevel protractor to measure the angle and the depth of holes, slots, and other internal features. A bevel protractor is set to measure an angle of 72°. What is the measure of the angle in standard position of the lower half of the ruler, used for measuring the depth of an object?

Solution :

To find the angle in standard position, we have to notice that the terminal arm is in which quadrant.

The terminal arm lies in the third quadrant. So the required angle will be 180 + 72. That is 252.

Problem 3 :

Researcher Mohammed Abubaker developed a circular periodic table. He claims that his model gives a better idea of the size of the elements. Joshua and Andrea decided to make a spinner for the circular periodic table to help them study the elements for a quiz. They will spin the arm and then name the elements that the spinner lands on. Suppose the spinner lands so that it forms an angle in standard position of 110°. Name one of the elements it may have landed on.

Solution :

In order to create an angle 110 degree, the arm has to landed at Cu, Ag, Au, Unn.

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