Answer:
The distance from the base of the statue to the ship is 771.60 ft
Step-by-step explanation:
Refer the attached figure
Height of statue AB= 250 feet
The tourist sees a ship coming into the harbor and measures the angle of depression as 18°.
So, ∠ACB = 18°
We are supposed to find the distance from the base of the statue to the ship i.e. BC
In ΔABC
BC=771.60 ft
Hence the distance from the base of the statue to the ship is 771.60 ft
So remember that the area of a trapezoid is , with b = bases and h = height. Before we can do the equation, however, we have to find the height. Using the right triangle, we can use the pythagorean theorem, which is
.
Since we know that the hypotenuse is 13 and one of the legs is 12, we can solve for the other leg. Our equation will look like this:
Firstly, solve the exponents:
Next, subtract 144 on both sides:
Next, square root both sides, and your height will be: x = 5
Now that we know both the height, 5, and the bases, 30 and 40, we can solve for the area of the trapezoid. Our equation will look like this:
Firstly, combine everything on the numerator:
Next, divide the fraction:
Next, multiply, and your answer will be A = 175 un^2.