Question

solve the height and distnace ​

Answer 1

SEE THE AATACHMENT YOUR ANSWER IS THIS AND I THINK IT IS CORRECT

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Answer 2

Answer

Distance between the two ships is 54.9 m

Solution

Let AB is the given light house of 75 m and angle B is 90° .C and D are the two ships.

From point A there is angle of depression of 45° and 30 ° at D and C point respectively.

Now we have to find out the distance between the two ships.

In right angled ∆ ABC.

Let BC = x

(angleB = 90°)

Height of light house (AB) (p)= 75m

Distance of point C from.(b) = x m

foot of light house (BC)

Angle C. (theta). = 30°

As we know that

perpendicular(p)/base(b) = tan theta

Applying this formula

==>

AB/CB = tan 30°

75/X = 1/√3. ( tan 30° = 1/√3)

75√3 = X

So we got the value of X

Now in ∆ ADB

Let DB as y

Height of light house (p) = 75m

Base of ∆ ADB (b). = y

Angle D (theta). = 45°

Now again applying the above mentioned formula.

P/b = tan theta

AB/DB = tan 45°

75 / y = 1. ( tan 45°=1)

75 = y

Here we got the value of y.

Now as mentioned in the question we have to find out the value of CD i.e distance between the two ships.

To find CD

CD = CB - DB

CD = 75√3 - 75

CD = 75(√3-1)

CD = 75(1.732 - 1). ( √3 = 1.732)

CD = 75( 0.732)

CD = 54.9 m

So the distance between the two ships is 54.9 m