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A 10-meter tall pole casts a shadow of 5 meters long. What is the angle of eleva
A 10-meter tall pole casts a shadow of 5 meters long. What is the angle of elevation of the sun?
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Practice Questions
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Q1
A 10-meter tall pole casts a shadow of 5 meters long. What is the angle of elevation of the sun?
30 degrees
45 degrees
60 degrees
75 degrees
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tan(angle) = height/shadow = 10/5 = 2, angle = 60 degrees.
Questions & Step-by-step Solutions
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Q
Q: A 10-meter tall pole casts a shadow of 5 meters long. What is the angle of elevation of the sun?
Solution:
tan(angle) = height/shadow = 10/5 = 2, angle = 60 degrees.
Steps: 7
Show Steps
Step 1: Identify the height of the pole, which is 10 meters.
Step 2: Identify the length of the shadow, which is 5 meters.
Step 3: Use the tangent function, which relates the angle of elevation to the height and shadow length. The formula is tan(angle) = height / shadow.
Step 4: Substitute the values into the formula: tan(angle) = 10 / 5.
Step 5: Calculate the right side: 10 divided by 5 equals 2, so tan(angle) = 2.
Step 6: To find the angle, use the inverse tangent function (also called arctan) on the value 2: angle = arctan(2).
Step 7: Use a calculator or a trigonometric table to find the angle. The angle is approximately 60 degrees.
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