Question

After launching, a model rocket is found to be 135 meters in a straight line from where it launched at an angle of 63° from the ground. How high is the rocket? What is the horizontal distance of the rocket?

a. Additional information needed
b. 135 meters high, 0 meters horizontal
c. 0 meters high, 135 meters horizontal
d. Cannot be determined without more data

Answer 1

The height and horizontal distance of the rocket from the launch point can be calculated using trigonometry with the given hypotenuse of 135 meters and the angle of elevation of 63°. The height is found using the sine function and the horizontal distance by the cosine function.

Step-by-step explanation:

To determine how high the rocket is and the horizontal distance, we can use trigonometric functions. The description provides us with the hypotenuse (the straight-line distance from the launch point to the rocket) of 135 meters and the angle of elevation at 63°. Using basic trigonometry:

• The height (opposite side) can be found using the sine function: height = hypotenuse × sin(angle) = 135 m × sin(63°).
• The horizontal distance (adjacent side) can be calculated using the cosine function: horizontal distance = hypotenuse × cos(angle) = 135 m × cos(63°).

After calculating these, we will have the values for the rocket's height and horizontal distance from the launch point.