Question

Kevin is launching a toy rocket. For safety reasons, he stands 42 yards away from the rocket before it is launched. He observes that the rocket hits its maximum height at an angle elevation of 46 °. What is the height the rocket reaches? Round to the nearest tenth.

Answer 1

The height of the rocket = 43.49 yards.

Explanation:

For better understanding of the solution, see the attached figure :

Let donate the angle of elevation by θ , it is the angle formed between the horizontal and the line of sight.

The height of the rocket will be perpendicular to the ground so a right angled triangle can be formed as shown in the figure.

Now, in ΔABC

`\tan\theta=(Perpendicular)/(Base)\\\\\tan 46\degrees=(AB)/(42)\\\\\implies AB=\tan 46\degrees* 42\\\\\bf\implies AB=43.49\thinspace{ yards}`

Hence, The height of the rocket = 43.49 yards.