Question

. Depression angle of a boat from 15 m high bridge is
45°. If boat is coming with the speed of 6 km/h. Then,
it will reach below the bridge in
​

Answer 1

AnswEr:—

• It would take 9 secs to reach below the bridge.

SteP By SteP ExplainaTion:—

refer to the attachment first,

$\large{\underline{\mathfrak{Given:-}}}$

• AB = 15 m ( height of the bridge)
• Angle ABC = 45°
• Speed of the boat = 6 km/h = 6×5/18 = 5/3 m/s

$\large{\underline{\mathfrak{To\:find:-}}}$

• Time taken by boat to reach below the bridge.

$\large{\underline{\mathfrak{Solution:-}}}$

Considering the ∆ABC,

$\longrightarrow$ AB/BC = tan 45°

$\longrightarrow$ 15/BC = 1 ( tan 45° = 1)

$\longrightarrow$ BC = 15 m ....(1)

Now, as we know,

$\longrightarrow$speed = distance/time

Let the time be 't',

$\longrightarrow$5/3 = 15/t

$\longrightarrow$ t = 15×3/5

$\longrightarrow$ t = 3×3

$\longrightarrow$ 9 secs.

$\large{\underline{\overline{\mathbb{HOPE\:IT\:HELPS\:UH!}}}}\huge{\ddot\smile}$

Answer 2

Given :-

• Angle of Depression = 45° .
• Height of Bridge = 15m.
• Speed of Boar = 6KM/H .

Solution :-

From image we can see That :-

→ ∆ABC is Right Angle ∆, Right angle At B.

→ Boat is at Point C.

→ BC = Distance Cover by boat to Reach below Bridge.

→ AB = Height of Bridge = 15m.

→ ∠ACB = 45°

So, we can Say That :-

→ Tan45° = AB/BC = Perpendicular / Base

→ 1 = 15/BC

→ BC = 15m.

Hence, we can say That, The boat Has to Cover a distance of 15m To reach below Bridge.

_____________________

Now,

→ Speed of Boat = 6km/h = 6 * (5/18) = (5/3)m / sec.

→ Distance = 15m.

So,

→ Time = (Distance/Speed)

→ Time = 15/(5/3)

→ Time = 15 * (3/5)

→ Time = 9 seconds.

Hence, The Boat will reach below the bridge in 9 Seconds.