1
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
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 cos A + cos B + cos C equal to ?

A
1
B
$\frac{41}{25}$
C
$\frac{37}{25}$
D
$\frac{33}{25}$
2
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
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 ?

A
$\frac{\text{x−y}}{2\sqrt{3}}$
B
$\frac{\text{x−y}}{4\sqrt{3}}$
C
$\frac{\text{x−y}}{4}$
D
$\frac{\text{x−y}}{2}$
3
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
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.

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

A
2 + $\frac{\sqrt{3}(\text{x−y})}{\text{x+y}}$
B
2 − $\frac{\sqrt{3}(\text{x−y})}{\text{x+y}}$
C
2 + $\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}$
D
2 − $\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}$
4
NDA Mathematics 4 September 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
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.

What is the length of the tower ?

A
$\frac{\text{x−y}}{2 \sqrt{3}} \sqrt{1+\left\{2+\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}\right\}^2}$
B
$\frac{\text{x−y}}{2 \sqrt{3}} \sqrt{1+\left\{2−\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}\right\}^2}$
C
$\frac{\text{x−y}}{4 \sqrt{3}} \sqrt{1+\left\{2+\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}\right\}^2}$
D
$\frac{\text{x−y}}{4 \sqrt{3}} \sqrt{1+\left\{2−\frac{\sqrt{3}(\text{x+y})}{\text{x−y}}\right\}^2}$
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