NDA 2019 Paper 1 | Height and Distance Question 13 | Mathematics

The angle of elevation of a tower of height h from a point A due South of it is x and from a point B due East of A is y. If AB = z, then which one of the following is correct?

h² (cot²y $$-$$ cot²x) = z²

z² (cot²y $$-$$ cot²x) = h²

h² (tan²y $$-$$ tan²x) = z²

z² (tan²y $$-$$ tan²x) = h²

NDA Mathematics 13 April 2025

MCQ (Single Correct Answer)

+2.5

-0.833

Consider the following for the two (02) items that follow:
The top (M) of a tower is observed from three points P, Q and R lying in a horizontal straight line which passes directly along the foot (N) of the tower. The angles of elevations of M from P, Q and R are 30°, 45° and 60° respectively. Let PQ = a and QR = b

What is PN equal to?

$ \left(\frac{3-\sqrt{3}}{2}\right)a$

$ \left(\frac{3+\sqrt{3}}{2}\right)a$

$ \left(\frac{3-\sqrt{3}}{4}\right)a$

$ \left(\frac{3+\sqrt{3}}{4}\right)a$

NDA Mathematics 13 April 2025

MCQ (Single Correct Answer)

+2.5

-0.833

What is MN equal to?

$ \left(\frac{3+\sqrt{3}}{2}\right)b$

$ \left(\frac{3-\sqrt{3}}{2}\right)b$

$ \left(\frac{3-\sqrt{3}}{4}\right)b$

$ \left(\frac{3+\sqrt{3}}{4}\right)b$

NDA Mathematics 13 April 2025

MCQ (Single Correct Answer)

+2.5

-0.833

A man at M, standing

100

m away from the base (P) of a chimney of height

50

m, observes the angle of elevation of the highest point (Q) of the smoke to be

4 5^{\circ}

. The highest point of the chimney is at R. Further P, R and Q are in a straight line and the straight line is perpendicular to PM. What is the angle RMQ equal to?

tan⁻¹($\frac{1}{2}$)

tan−1($\frac{1}{3}$​)

tan⁻¹($\frac{2}{3}$)

tan⁻¹($\frac{3}{4}$)

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