Answer:
45.54m
Step-by-step explanation:
Refer the attached figure
Scarlett's height = AB = 1.65 meters
She stands 90 meters away from the dam i.e. BE = AC = 90 m
She records the angle of elevation to the top of the dam to be 26º i.e. ∠DBE = 26°
Height of the Dam = DC = EC+DE
AB = EC = 1.65
In ΔBDE
[tex]Tan \theta = \frac{Perpendicular}{Base}[/tex]
[tex]Tan 26^{\circ} = \frac{DE}{BE}[/tex]
[tex]Tan 26^{\circ} = \frac{DE}{90}[/tex]
[tex]0.48773 \times 90=DE[/tex]
[tex]43.89=DE[/tex]
Height of the Dam = DC =1.65+43.89=45.54 m
Hence the height of the dam is 45.54 m.
Answer:
The height of the dam is 45.54 m.
Step-by-step explanation:
Given : Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26º. Scarlett's height is 1.65 meters.
To find : The height of the dam ?
Solution :
Refer the attached figure to clear the image of question.
The Scarlett's height be EC= 1.65 meters
She stands 90 meters away from the dam i.e. DE = BC = 90 m
The angle of elevation to the top of the dam to be 26º i.e. ∠BCA = 26°
Now,
Height of the Dam is AD = BD+AB
As, BD = EC = 1.65
We apply trigonometry, In ΔABC
[tex]\tan \theta = \frac{\text{Perpendicular}}{\text{Base}}[/tex]
[tex]\tan26^{\circ} = \frac{DE}{BE}[/tex]
[tex]\tan26^{\circ} =\frac{DE}{90}[/tex]
[tex]0.48773 \times 90=DE[/tex]
[tex]DE=43.89[/tex]
Substitute the value,
Height of the Dam is AD=1.65+43.89=45.54 m
Therefore, the height of the dam is 45.54 m.
