From a boat on the river below a dam, the angle of elevation to the top of the dam is 29deg6'. If the dam is 2430 feet above the level of the river, how far is the boat from the base fo the dam(to the nearest foot)?
my answer came out as 4366 feet.
am i right:(
yup, very good.
To determine the distance from the boat to the base of the dam, we can make use of the trigonometric function tangent.
First, let's convert the angle of elevation to decimal degrees. To do this, we add the number of minutes divided by 60 to the angle in degrees:
29 + (6/60) = 29.1 degrees
Now, let's label the distance from the boat to the base of the dam as "x."
We can set up a right triangle, where the opposite side is the height of the dam (2430 feet) and the adjacent side is the distance from the boat to the base of the dam (x feet). The angle opposite the height of the dam is 29.1 degrees.
Using the tangent function, we can write the equation as:
tan(29.1) = 2430 / x
To solve for x, we can rearrange the equation:
x = 2430 / tan(29.1)
Using a calculator, we can calculate the value of x:
x ≈ 4365.973
Therefore, the distance from the boat to the base of the dam, rounded to the nearest foot, is 4366 feet.
Your answer of 4366 feet is correct.