Question

15. From a lighthouse of height 60 ft above sea level, an observer sees the angle of depression of a ship change from 37° to 53° in 20 seconds. Find the speed of the ship assuming it is uniform.

Answer 1

||✪✪ QUESTION ✪✪||

From a lighthouse of height 60 ft above sea level, an observer sees the angle of depression of a ship change from 37° to 53° in 20 seconds. Find the speed of the ship assuming it is uniform. ? (Excellent Question ).

|| ✰✰ ANSWER ✰✰ ||

❁❁ Refer To Image First .. ❁❁

|| ★★ FORMULA USED ★★ ||

☛ Ratio of Sides of A Right ∆ with angle 90°-53°-37° is 5 - 4 - 3.⟦Always Remember This .⟧

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Now, From image, we can see That ,

In Right ∆ABD, we have :-

➾ AB = 60 Ft.

➾ ∠ABD = 90°

➾ ∠ADB = 53°

➾ ∠BAD = 180°-(90+53) = 37°

So ,

➼ Tan@ = Perpendicular /Base

➼ Tan53° = AB/BD

➼ Tan53° = (4/3) = (60/BD)

➼ (4/3) = (60/BD)

➼ 4BD = 3*60

➼ BD = (180/4)

➼ BD = 45Ft. ------------------ Equation ❶.

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Similarly, In Right ∆ABC, we Have :-

➳ AB = 60Ft.

➳ ∠ABC = 90°

➳ ∠ACB = 37°

➳ ∠BAC = 180° - (90+37) = 53°

So,

➻ Tan37° = AB/BC

➻ (3/4) = (60/BC)

➻ 3BC = 60*4

➻ BC = (240/3)

➻ BC = 80 Ft. ----------------- Equation ❷

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Now,

➺ BC = BD + DC

Putting Both Values from Equations ❶ & ❷ we get,

➺ 80 = 45 + DC

➺ DC = 80 - 45

➺ DC = 35 ft.

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Now, we Have Given That, The Ship cover DC distance in 20 seconds.

Hence,

☞ Speed = (Distance/Time).

☞ Speed = (35/20)

☞ Speed = 1.75Ft/seconds.

Hence, Speed of Ship is 1.75ft/seconds.

Answer 2

AnSwEr:—

$\longrightarrow$⟩ 1.75ft/s

$\rule{200}2$

SteP By SteP ExplainaTion:—

Consider ∆ABC (refer to the image)

$\longrightarrow$»AB = 60 ft

$\longrightarrow$» $\angle$ ABC = 53°

$\longrightarrow$»Let BC be x

So,

$\longrightarrow$»AB/BC = tan53° (tan53°=4/3)

$\longrightarrow$»60/x= 4/3

$\longrightarrow$» x= 45 ft

BC= 45ft

Now,

consider∆ ABD

$\longrightarrow$»AB= 60 ft

$\longrightarrow$» $\angle$ 37°

$\longrightarrow$» AB/BD= tan 37°

$\longrightarrow$» let BD be y

$\longrightarrow$» 60/y = 3/4 (tan37°= 3/4)

$\longrightarrow$» 60×4/3 = y

$\longrightarrow$» y = 80 ft

Now, CD = BD - BC

$\longrightarrow$» 80-45

$\longrightarrow$» 35 ft

Now, speed = distance/Time

$\longrightarrow$»35/20

$\longrightarrow$» 1.75 ft/s

$\rule{200}2$