Answer:
77 m (nearest metre)
Step-by-step explanation:
Angle of Elevation
If a person stands at a point and looks up at an object, the angle between their horizontal line of sight and the object is called the angle of elevation.
To find how tall the flagpole is, model as a right triangle and solve using the tan trigonometric ratio.
Tan trigonometric ratio
[tex]\sf \\tan(\theta)=\dfrac{O}{A}[/tex]
where:
- [tex]\theta[/tex] is the angle
- O is the side opposite the angle
- A is the side adjacent the angle
Given information:
- Person height = 1.6 m
- Horizontal distance (from person to flagpole) = 35 m
- Angle of elevation = 65°
Therefore:
- [tex]\theta[/tex] = 65°
- O = height of flagpole less height of person
- A = 35 m
As the person is 1.6 m tall, we model the line of sight as 1.6 m above ground level. Therefore, when calculating the height of the flagpole, we will need to add the height of the person to the value found using the trig ratio.
Substitute the given values into the formula and solve for O:
[tex]\implies \sf \tan(65^{\circ})=\dfrac{O}{35}[/tex]
[tex]\implies \sf O=35\tan(65^{\circ})[/tex]
Therefore the height of the flagpole is:
[tex]\implies \sf 35\tan(65^{\circ})+1.6=76.65774222...[/tex]
[tex]\implies \sf Height\:of\:flagpole=77\:m\:(nearest\:metre)[/tex]
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