Solve the problem.
-A rocket is fired at an angle of $21 ^ { \circ }$ with the ground. Find the distance traveled by the rocket when it has reached an altitude of 175 feet. Give your answer to the nearest foot.
A) 488 feet
B) 163 feet
C) 67 feet
D) 63 feet

Question

Quizplus · Accepted Answer

To find the distance traveled by the rocket when it reaches an altitude of 175 feet, we can use trigonometry. The altitude forms the opposite side of a right triangle, and we want to find the hypotenuse (the distance traveled). Using the sine function, $\sin(21^\circ) = \frac{opposite}{hypotenuse}$, we can solve for the hypotenuse: $hypotenuse = \frac{opposite}{\sin(21^\circ)} = \frac{175}{\sin(21^\circ)}$. Calculating this gives a value close to 488 feet, rounding to the nearest foot.

Solve the Problem 21∘21 ^ { \circ }21∘ With the Ground

Solve the Problem $21 ^ { \circ }$ With the Ground