The illustration depicts two hills of different heights LM and TP. When the top T of the second hill is viewed from the top L of the first hill, the angle of depression is 30. When the top T is viewed from the foot M of the first hill, the angle of elevation is 60. If the distance between points M and P is 500 feet, what is the difference between the heights of the two hills?a)500/3b)600/3c)500/2d)800/3e)1000/3Correct answer is option 'A'. Can you explain this answer?

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The illustration depicts two hills of different heights LM and TP. When the top T of the second hill is viewed from the top L of the first hill, the angle of depression is 30°. When the top T is viewed from the foot M of the first hill, the angle of elevation is 60°. If the distance between points M and P is 500 feet, what is the difference between the heights of the two hills?

a)
500/√3
b)
600/√3
c)
500/√2
d)
800/√3
e)
1000/√3

Correct answer is option 'A'. Can you explain this answer?

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The illustration depicts two hills of different heights LM and TP. Whe...

Step 1: Question statement and Inferences

The question asks us to find the length of NL.

Let NL = x feet

We are given that the angle between the horizontal and a person’s line of sight when he looks at point T from point L is 30^o.

This means, in right triangle LNT, Angle NTL = 30∘

Let’s depict this information in the figure:

Step 2: Finding required values

By applying the Angle Sum Property in right triangle LNT, we get

Angle TLN = 60°

Thus Triangle LNT is a 30°-60°-90° triangle. In a 30°-60°-90° triangle, the sides opposite to the angles 30°, 60°, and 90° respectively are in the ratio 1 : √3 : 2

That is, LN: NT : TL = 1 : √3 : 2

Also, in quadrilateral MPTN, lines MN and PT are both drawn perpendicular to the same line MP. Therefore, lines MN and PT are parallel to one another. Also, line NT is perpendicular to the vertical line MN; therefore, line NT is parallel to the horizontal line MP.

Thus, quadrilateral MPTN is made up of two sets of parallel lines and the enclosed angle is 90°

This means, quadrilateral MPTN is a rectangle.

Now, the opposite sides of a rectangle are equal.

Therefore, NT = MP = 500 feet

Step 3: Calculating the final answer

Therefore,

Hence, the correct answer is Option A

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The illustration depicts two hills of different heights LM and TP. When the top T of the second hill is viewed from the top L of the first hill, the angle of depression is 30°. When the top T is viewed from the foot M of the first hill, the angle of elevation is 60°. If the distance between points M and P is 500 feet, what is the difference between the heights of the two hills?a)500/√3b)600/√3c)500/√2d)800/√3e)1000/√3Correct answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The illustration depicts two hills of different heights LM and TP. When the top T of the second hill is viewed from the top L of the first hill, the angle of depression is 30°. When the top T is viewed from the foot M of the first hill, the angle of elevation is 60°. If the distance between points M and P is 500 feet, what is the difference between the heights of the two hills?a)500/√3b)600/√3c)500/√2d)800/√3e)1000/√3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The illustration depicts two hills of different heights LM and TP. When the top T of the second hill is viewed from the top L of the first hill, the angle of depression is 30°. When the top T is viewed from the foot M of the first hill, the angle of elevation is 60°. If the distance between points M and P is 500 feet, what is the difference between the heights of the two hills?a)500/√3b)600/√3c)500/√2d)800/√3e)1000/√3Correct answer is option 'A'. Can you explain this answer?.

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