Question

find the distance between two points A and B on opposite side of a river , a serveyor runs along line ac is parallel to ab by measurement he finds ac= 200m and angle abc=45°​

Answer 1

Answer:-

Let AB is tower and two points C and D are present same side of tower as shown in figure.

Let the distance between C and D is d .

And the distance between tower and point C is x

Now, ∆ABC ,

Here ∠ACB = 60°

So, apply tan∠ACB = tan60° = AB/BC

AB is given e.g., AB = 15m

∴ tan60° = √3 = 15/BC

⇒BC = 15/√3 = 5√3 m

Now, for ∆ABD

∠ADB = 45°

Apply tan∠ADB = tan45° = AB/BD

⇒ 1 = 15/(BC + CD)

⇒BC + CD = 15m

Put BC = 5√3m

∴ CD = 15m - BC = 15m - 5√3m

Hence, distance between C and D = 5√3(√3 - 1)m

Answer 2

Step-by-step explanation:

.Answer:-

Let AB is tower and two points C and D are present same side of tower as shown in figure.

Let the distance between C and D is d .

And the distance between tower and point C is x

Now, ∆ABC ,

Here ∠ACB = 60°

So, apply tan∠ACB = tan60° = AB/BC

AB is given e.g., AB = 15m

∴ tan60° = √3 = 15/BC

⇒BC = 15/√3 = 5√3 m

Now, for ∆ABD

∠ADB = 45°

Apply tan∠ADB = tan45° = AB/BD

⇒ 1 = 15/(BC + CD)

⇒BC + CD = 15m

Put BC = 5√3m

∴ CD = 15m - BC = 15m - 5√3m

Hence, distance between C and D = 5√3(√3 - 1)m

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