NDA Mathematics 16 April 2023 | Height and Distance Question 15 | Mathematics

A flagstaff 20 m long standing on a pillar 10 m high subtends an angle tan^-1(0.5) at a point P on the ground. Let θ be the angle subtended by the pillar at this point P.

What is a possible value of tan θ ?

$\frac{3}{4}$

$\frac{2}{3}$

$\frac{1}{3}$

$\frac{1}{4}$

NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

ABC is a triangular plot with AB = 16 m, BC = 10 m and CA = 10 m. A lamp post is situated at the middle point of the side AB. The lamp post subtends an angle 45° at the vertex B.

What is the height of the lamp post ?

6 m

7 m

8 m

9 m

NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

There are two points P and Q due south of a leaning tower, which leans towards north. P is at a distance x and Q is at distance y from the foot of the tower (x > y). The angles of elevation of the top of the tower from P and Q are 15° and 75° respectively.

At what height is the top of the tower above the ground level ?

$\frac{\text{x−y}}{2\sqrt{3}}$

$\frac{\text{x−y}}{4\sqrt{3}}$

$\frac{\text{x−y}}{4}$

$\frac{\text{x−y}}{2}$

NDA Mathematics 4 September 2022

MCQ (Single Correct Answer)

+2.5

-0.83

If θ is the inclination of the tower to the horizontal, then what is cot θ equal to ?

2 + $\frac{\sqrt{3}(\text{x−y})}{\text{x+y}}$

2 − $\frac{\sqrt{3}(\text{x−y})}{\text{x+y}}$

2 + $\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}$

2 − $\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}$

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