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Re: The angle of elevation of the top of a lighthouse 60 m high, from two [#permalink]
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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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Re: The angle of elevation of the top of a lighthouse 60 m high, from two [#permalink]
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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


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)
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Re: The angle of elevation of the top of a lighthouse 60 m high, from two [#permalink]
1
Kudos
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
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Re: The angle of elevation of the top of a lighthouse 60 m high, from two [#permalink]
1
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Quote:
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



Ans is C , imo.
Please refer to attachment .
Attachments

File comment: Solution -figure
12_june.png
12_june.png [ 52.68 KiB | Viewed 3755 times ]

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The angle of elevation of the top of a lighthouse 60 m high, from two [#permalink]
Top Contributor
Bunuel wrote:

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


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

B to D = 60 m [as angle B and angle BAD= 45 degrees]

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.
Attachments

TRIANGLE.png
TRIANGLE.png [ 7.41 KiB | Viewed 3548 times ]

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Re: The angle of elevation of the top of a lighthouse 60 m high, from two [#permalink]
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Re: The angle of elevation of the top of a lighthouse 60 m high, from two [#permalink]
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