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
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.