Answer:
83 m (nearest metre)
Step-by-step explanation:
This can be modeled as a right triangle, where the base is 60 m and the height is the height of the building.
Alternate Interior Angles Theorem (Z-angles)
If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.
Using the Alternate Interior Angles theorem, the angle between the ground and the dashed line (angle of elevation) is 54°.
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:
- [tex]\theta[/tex] = 54°
- O = height of building (h)
- A = 60
Substituting the given values into the formula and solving for h:
[tex]\implies \sf \tan(54^{\circ})=\dfrac{h}{60}[/tex]
[tex]\implies \sf h=60 \tan(54^{\circ})[/tex]
[tex]\implies \sf h=82.58291523...[/tex]
[tex]\implies \sf h=83\:\:m\:(nearest\:metre)[/tex]
