A man is standing near the Washington Monument, observing its …

Mathematics Questions
Short Answer
Step by Step Solution
Mathematics Questions

A man is standing near the Washington Monument, observing its 555-foot height at a 60¬¨‚àû angle of elevation. Given that the monument and the ground form a right angle, which measurements are accurate based on this scenario? Check all that apply: 1) The distance from the man’s feet to the base of the monument is 185‚Äöao3 feet. 2) The distance from the man’s feet to the top of the monument is 370‚Äöao3 feet. 3) The distance from the man’s feet to the top of the monument is 1,110 feet. 4) The distance from the man’s feet to the base of the monument is 277.5 feet. 5) The segment representing the monument’s height is the longest segment in the triangle.

Short Answer

The first step involves determining the distance to the base of the monument using the formula Distance = 555 √∑ tan(60¬∞), resulting in a distance of 185‚ao3 feet. The second step calculates the distance to the top using the sine function, giving a hypotenuse of 370‚ao3 feet, confirming alignment with options A and B.

Step-by-Step Solution

Step 1: Determine the Distance to the Base of the Monument

To find the distance from the man’s feet to the base of the monument, you need to use the formula involving the tangent of the angle. The calculation follows:

  • Distance = 555 ‚àö‚àë tan(60¬¨‚àû)
  • This simplifies to Distance = 555 ‚àö‚àë ‚Äöao3
  • Finally, you calculate Distance = 185‚Äöao3 feet.

Step 2: Calculate the Distance to the Top of the Monument

The next step is to find the distance from the man’s feet to the top of the monument using the sine function. This involves evaluating the height based on the hypotenuse:

  • Hypotenuse = 555 ‚àö‚àë sin(60¬¨‚àû)
  • This becomes Hypotenuse = 555 ‚àö‚àë (‚Äöao3/2)
  • Through simplification, you arrive at Hypotenuse = 1110 ‚àö‚àë ‚Äöao3.

Step 3: Final Measurements and Conclusion

At this point, you convert the hypotenuse distance to a more recognizable format. Hence, the distance from the man’s feet to the top of the monument is:

  • Hypotenuse = 370‚Äöao3 feet.
  • Comparing both calculated distances confirms that the correct options align with A and B.

Related Concepts

Tangent

A trigonometric function that relates the angle of a right triangle to the ratio of the length of the opposite side to the length of the adjacent side

Sine

A trigonometric function that relates the angle of a right triangle to the ratio of the length of the opposite side to the length of the hypotenuse

Hypotenuse

The longest side of a right triangle, opposite the right angle, which can be calculated using other sides and angles of the triangle.

Table Of Contents
  1. A man is standing near the Washington Monument, observing its 555-foot height at a 60¬∞ angle of elevation. Given that the monument and the ground form a right angle, which measurements are accurate based on this scenario? Check all that apply: 1) The distance from the man's feet to the base of the monument is 185‚ao3 feet. 2) The distance from the man's feet to the top of the monument is 370‚ao3 feet. 3) The distance from the man's feet to the top of the monument is 1,110 feet. 4) The distance from the man's feet to the base of the monument is 277.5 feet. 5) The segment representing the monument's height is the longest segment in the triangle.

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