The distance between Casey and the base of the lighthouse is 49 ft.
What is the angle of elevation and depression?
The angle of elevation refers to the angle formed by the straight horizontal line and an object. The crosshair of an observer is usually above the horizontal.
The angle of depression is the angle formed by the horizontal and a downward angle to an object. The crosshair of an observer is usually above below the horizontal.
1.
The distance between Casey and the base of the lighthouse can be determined by using the tangent of trigonometry.
(TOA)
[tex]\mathbf{tan \theta = \dfrac{opp}{adj}}[/tex]
[tex]\mathbf{tan \ 58 = \dfrac{78}{x}}[/tex]
[tex]\mathbf{x= \dfrac{78}{1.6003}}[/tex]
x ≅ 49 ft
2.
The height of the goal post can be determined by using the tangent of trigonometry.
[tex]\mathbf{tan \theta = \dfrac{opp}{adj}}[/tex]
[tex]\mathbf{tan 17 = \dfrac{x}{131}}[/tex]
x = (tan 17) × 131
x = 0.3057 × 131
x ≅ 40 ft
3.
The horizontal distance between Zack and the water fountain is calculated by using the tangent of trigonometry.
[tex]\mathbf{tan \theta = \dfrac{opp}{adj}}[/tex]
[tex]\mathbf{tan \ 28 = \dfrac{75}{x}}[/tex]
[tex]\mathbf{x = \dfrac{75}{0.5317}}[/tex]
x = 141 ft
Learn more about the angle of elevation and depression here:
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