DRAWING ANGLES WITH A PROTRACTOR
When planning the Apollo 11 voyage, NASA scientists made a flight plan for the trip, including a step-by- step process to get the moon lander to the appointed spot on the surface. Katherine Johnson and her team calculated a series of angles for the moon lander to make before its descent. An angle is a figure made by two rays (a line with one endpoint) that meet at a point called a vertex. The difference between the two lines is measured in degrees.
EXAMPLE: Draw an angle of 52°.
Draw a ray and label the endpoint Y and add another point on the ray labeled X :
x
y
z
Align the baseline of your protractor with the ray. Point Y should be at your protractor’s origin. Make a point along the scale of the protractor at 52° and label it Z :
z
y
x
Draw a ray to connect point Y to point Z to complete the angle:
z
y
x
xyz
Name your angle using the points in the angle, with the vertex in the middle. This angle is ∠ XYZ .
y
x
Complete the diagram of the moon lander’s flight plan by drawing the angles that Johnson calculated. Line HMQ marks the horizon, or the line where the moon and sky appear to meet. Use point M (the moon’s surface) as the vertex for all angles.
✎
H
M
Q
1 The moon lander traveled from left to right. When it was 35° above the moon’s horizon line, it began its landing. Draw a ray with a point of B to create this angle. What’s this angle’s name?
toward the moon and had moved an additional 16° above the horizon. Draw a ray with point C to create a 16° angle above the angle you drew in No. 1. What is the name of this new angle?
94° from the angle you drew in No. 2. Draw a ray with point D to make the angle and name it.
4 What is the measurement of ∠ DMQ that you created? Explain how you determined this.
3 Another 75 seconds later, the spacecraft was in position to detach the lander at
2 Forty seconds later, the spacecraft began tilting
Student Handbook 47
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