A space shuttle is spotted flying at an angle of elevation of 17° when sighted from Cape Canaveral. At the moment it is sighted, it is directly overhead a ship located 12 mi from the Cape. The height of the shuttle at this moment is approximately
a)3.5
b)3.7
c)2.8
d)4.1
3.7 miles. The tangent of 17 degrees is .3057. So x over 12 = .3057 Thus x=(12)(.3057) or 3.6684 miles whch rounded off is 3.7 miles.
To solve this problem, we can use the concept of trigonometry. We will need to use the tangent function to find the height of the shuttle.
Let's break down the given information:
- The angle of elevation of the shuttle from Cape Canaveral is 17°.
- The shuttle is directly overhead a ship located 12 miles from the Cape.
Using the tangent function, we can set up the equation:
tan(17°) = height of the shuttle / distance from the ship to the Cape.
We know the distance from the ship to the Cape is 12 miles. Substituting this value into the equation, we have:
tan(17°) = height of the shuttle / 12
Now we need to solve for the height of the shuttle. Rearrange the equation:
height of the shuttle = 12 * tan(17°)
Using a calculator, evaluate tan(17°) and multiply it by 12:
height of the shuttle ≈ 4.1 miles
Therefore, the height of the shuttle is approximately 4.1 miles.
The correct answer is d) 4.1.