You stand 75.0 m away from the launch pad of a model rocket. you watch the rocket rise to an angle of 65.0 degrees. your eye is 1.50 m above the horizontal. what altitude did the rocket achieve

162.3 meters

Draw a diagram for the problem. You will have a right triangle with a base of 75.0 m and an angle of 65.0 degrees. You want the opposite side of the triangle x. Using the law of tangents, you have the following

x/75.0 = tan(65)

x = 75.0 * tan(65)

x = 75.0 * 2.144507

x = 160.8 meters

So now you know that the rocket went 160.8 meters above your eye. But your eye isn't at ground level, it's 1.50 meters higher. So add 1.50 meters to the 160.8, giving you 162.3 meters.