Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

A man standing in one corner of a square football field observes that the angle subtended by a pole in the corner just diagonally opposite to this corner is \( \Large 60 ^{\circ} \). When he retires 80 m from the corner, along the same straight line, he finds the angle to be \( \Large 30 ^{\circ} \). The length of the field is

A) 20 m
B) \( \Large 40\sqrt{2} \) m
C) 40 m
D) \( \Large 20\sqrt{2} \) m

Correct Answer:



C) 40 m

Description for Correct answer:

From the figure,

Let the length of football field = l m

Height of the pole = x m

Therefore, In \( \Large \triangle ABC, \tan 60 =\frac{x}{l} \)

\( \Large \sqrt{3}=\frac{x}{l}; x=\sqrt{3}l \)

Now, in \( \Large \triangle ABD \)

\( \Large \tan 30 ^{\circ} =\frac{x}{l+80} => \frac{1}{\sqrt{3}} = \frac{x}{l+80} \)

\( \Large l + 80 = \sqrt{3}x \)

Now, from Eq. (i), we get

\( \Large l + 80 = \sqrt{3} \left(\sqrt{3} l\right) \)

=> \( \Large l + 80 = 3l => 80 = 3l - l \)

\( \Large \therefore\ l = \frac{80}{2} = 40 m \)

Part of solved Height and Distance questions and answers : >> Elementary Mathematics >> Height and Distance

Comments

Similar Questions

1). A spherical balloon of radius r subtends angle \( \Large 60 ^{\circ} \) at the eye of an observer. If the angle of elevation of its centre is \( \Large 60 ^{\circ} \) and h is the height of the centre of the balloon, then which one of the following is correct?

A). h=r

B). \( \Large h = \sqrt{2}r \)

C). \( \Large h = \sqrt{3}r \)

D). h=2r

2). If the roots of equations \( \Large ax^{2}+bx+c=0 \) be \( \Large \ \alpha \ and\ \beta \) then the roots of equations \( \Large cx^{2}+bx+a=0 \) are:

A). \( \Large - \alpha ,\ - \beta \)

B). \( \Large \alpha ,\ \frac{1}{ \beta } \)

C). \( \Large \frac{1}{ \alpha },\ \frac{1}{ \beta } \)

D). none of these

3). Both the roots of the given equation. \( \Large \left(x-a\right) \left(x-b\right)+ \left(x-b\right) \left(x-c\right)+ \left(x-c\right) \left(x-a\right)=0 \) are always

A). positive

B). negative

C). real

D). imaginary

4). If the difference of roots of the equation \( \Large x^{2}-bx+c=0 \) be 1, then;

A). \( \Large b^{2}-4c-1=0 \)

B). \( \Large b^{2}-4c=0 \)

C). \( \Large b^{2}-4c+1=0 \)

D). \( \Large b^{2}+4c-1=0 \)

5). If \( \Large 2+i\sqrt{3} \) is a root of the equation \( \Large x^{2}+px+q=0 \) where p and q are real, then \( \Large p, q \) is equal to:

A). (-4, 7)

B). (4,-7)

C). (4, 7)

D). (-4, -7)

6). If \( \Large x=\sqrt{1+\sqrt{1+\sqrt{1}+.....}} \), the x is equal to

A). \( \Large \frac{1+\sqrt{5}}{2} \)

B). \( \Large \frac{1-\sqrt{5}}{2} \)

C). \( \Large \frac{1\pm \sqrt{5}}{2} \)

D). none of these .

7). If \( \Large \alpha , \beta \) are the roots of equation \( \Large ax^{2}+bx+c=0 \), then \( \Large \frac{ \alpha }{ \alpha \beta +b}+\frac{ \beta }{ \alpha x+b} \) is equal to

A). 2/a

B). 2/b

C). 2/c

D). -2/a

8). If the roots of the equation \( \Large \frac{ \alpha }{x- \alpha }+\frac{ \beta }{x- \beta }=1 \) be equal in magnitude but opposite in sign, then \( \Large \alpha + \beta \) is equal to:

A). 0

B). 1

C). 2

D). none of these

9). If the roots of the equation \( \Large px^{2}+2qx+r=0 \) and \( \Large qx^{2}-2\sqrt{pr}x+q=0 \) be real, then:

A). \( \Large p=q \)

B). \( \Large q^{2}=pr \)

C). \( \Large p^{2}=qr \)

D). \( \Large r^{2}=pq \)

10). If one root of the quadratic equation \( \Large ax^{2}+bx+c=0 \) is equal to nth power of the other root, then the value of \( \Large \left(ac^{n}\right)^{\frac{1}{n+1}} + \left(a^{n}c\right)^{\frac{1}{n+1}} \) is equal to

A). b

B). -b

C). \( \Large b^{1/n+1} \)

D). \( \Large -b^{1/n+1} \)