The angle of elevation of the top of a lighthouse 60 m high, from two

Question

Competition Mode Question

The angle of elevation of the top of a lighthouse 60 m high, from two points on the ground on its opposite sides are 45° and 60°. What is the distance between these two points?

A.  60+20\sqrt{3}  m

B. 90 m

C. 45 m

D.  20\sqrt{3}  m

E. 30 m

MayankSingh · Answer

IMO A
 
 Refer attached Image
Let AB = light house & C and D be two points on opposite side of AB
AB= 60m
∠ACB=45 & ∠ADB= 60

In right angled triangle ABC
tan 45 = AB/BC
AB=BC=60
 
In right angled triangle ADB
tan 60= AB/BD
√ 3= AB/BD
BD= 60/√ 3 = 20√ 3

Therefore, CD= 60+20√ 3

Ans A

Saasingh · Answer

IMO A.

We need to find distance AB.

In both traingles ACD and BCD , we see that perpendicular/base = tan(x).

Therefore, from triangle ACD, 60/AD = tan 45 = 1. 
AD = 60.

From triangle BCD, 60/DB= tab 60 = root3

DB = 60/root3 = 20*root3

So, AB = 60+20root3

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yashikaaggarwal · Answer

Height of lighthouse = 60. = P
Angle of elevation at one side = 45°
The distance between one point to light house= B
Tan 45° = P/B
1 = 60/B
B = 60 ---------(1)

Height of lighthouse = 60. = P
Angle of elevation at other side = 60°
The distance between second point to light house= B
Tan 60° = P/B
√3 = 60/B
B = 60/√3 = 20√3 ---------(1)

Distance between two points = Distance of one point to light house + Distance of second point to light house

=> D = 60+20√3

Answer is A

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exc4libur · Answer

Triangle 45: x,x,x√2=x,60,x√2
Triangle 60: y,y√3,2y=y,60,2y

x=60
y√3=60, =60/√3=60*√3/3=20√3

Distance between: 60+20√3

Ans (A)

Archit3110 · Answer

for two sides we get are two ∆ 45:45:90 and 30:60:90
so base of one side is 60 and other side is
60= x√3 ; x = 20√3
total base 60+20√3
OPTION A

The angle of elevation of the top of a lighthouse 60 m high, from two points on the ground on its opposite sides are 45° and 60°. What is the distance between these two points?

A. 60+203‾√60+203 m

B. 90 m

C. 45 m

D. 203‾√203 m

E. 30 m

HoneyLemon · Answer

Ans is C , imo. 
Please refer to attachment .

MHIKER · Answer

We need to find out the distance from B to C.

B to D = 60 m

D to C =  \frac{60}{\sqrt{3}}

Thus, B To C = 60+ \frac{60}{\sqrt{3}}

= 60+ \frac{60}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}}

=60+60* \frac{\sqrt{3}}{3}

= 60+20\sqrt{3}

The answer is A.

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The angle of elevation of the top of a lighthouse 60 m high, from two

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