A rocket is fired at sea level and climbs at a constant angle of 70° through a distance of 10,000 feet. Approximate its altitude to the nearest foot. how do you solve this?/
To solve this problem, we will use trigonometry and the concept of right triangles. Here are the steps to find the approximate altitude of the rocket:
1. Draw a right triangle: Start by drawing a triangle ABC, where B represents the starting point at sea level, and C represents the approximate altitude of the rocket. Angle ACB should be 70°.
2. Identify the known values: From the problem statement, we know that angle ACB is 70°, and the distance AB (the ground distance traveled by the rocket) is 10,000 feet.
3. Apply trigonometry: Since we want to find the altitude, we need to determine the length of side BC. In the right triangle ABC, the sine of angle ACB is defined as the ratio of the length of the side opposite to the angle (BC) to the length of the hypotenuse (AB). Therefore, we can use the sine function to find BC:
sin(70°) = BC / AB
rearranging the equation, we get:
BC = AB * sin(70°)
4. Substitute values and evaluate: Plug in the values AB = 10,000 feet and sin(70°) into the equation:
BC = 10,000 feet * sin(70°)
Use a calculator to find the approximate value of sin(70°) and then multiply it with 10,000 feet to find the altitude BC.
5. Round the result: Finally, round the calculated value of BC to the nearest foot to approximate the altitude of the rocket.
Following these steps, you should be able to calculate the approximate altitude of the rocket fired at sea level.