Answer:
The angle of elevation of the sun to the nearest hundredth of a degree is 44.07°
Step-by-step explanation:
Here is the complete question:
A building 86.53 feet tall has a shadow that is 89.39 feet long. Find the angle of elevation of the sun to the nearest hundredth of a degree.
Step-by-step explanation:
Please see the attachment below for an illustrative diagram:
From the diagram
/AC/ is the height of the building
/CB/ is the length of the shadow
/AC/ = 86.53 feet
/CB/ 89.39 feet
θ is the angle of elevation
Consider triangle ABC
/AC/ is the opposite
and /CB/ is the adjacent
From
tanθ =[tex]\frac{Opposite}{Adjacent}[/tex]
Then,
tanθ = [tex]\frac{/AC/}{/CB/}[/tex]
tanθ = [tex]\frac{86.53}{89.39}[/tex]
tanθ = 0.9680
∴θ = tan⁻¹(0.9680)
θ = 44.0686°
θ = 44.07° (to the nearest hundredth of a degree)
Hence, the angle of elevation of the sun to the nearest hundredth of a degree is 44.07°
