Question

Find the answer of the above question. Best answer will be marked as brainliest ​

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

( Refer To Image First.)

From image we have :-

→ AB = Tower .

→ BD = x m.

→ BC = (30 + x) m.

→ DC = 30m (Given).

Now, in Rt. ∆ABD we Have :-

→ Tan60° = AB / BD

→ √3 = AB / x

→ AB = √3x . ---------- Equation (1).

Similarly,

in Rt. ∆ABC, we Have :-

→ Tan30° = AB / BC

→ (1/√3) = AB / (x + 30)

→ √3AB = (x + 30)

→ AB = (x + 30) / √3

→ AB = { (x + 30) / √3} * (√3/√3)

→ AB = √3(x + 30) / 3 ------- Equation (2).

Comparing Both Equations Now, we get,

→ √3x = √3(x + 30) / 3

→ 3x = x + 30

→ 3x - x = 30

→ 2x = 30

→ x = 15 m.

Hence ,

→ Height of Tower = AB = √3x = √3 * 15 = 15√3 m (Ans).

Therefore, Height of Tower will be 15√3 m.

Answer 2

Solution:

AB is the tower and BC is the length of the shadow when the sun's altitude is 60° .The angle of elevation of the top of the tower from the tip of the shadow is 60° and DB is the length of the shadow ,When the angle of elevation is 30°

✿Now ,let be h m and BC be x m. According to the question,DB is 30m longer than BC.

so,

→DB = (40+x)

✿Now ,we have two right triangles ABC and ABD.

In∆ABC,

→tan60° = AB/BC

→√3 = h/x

In ∆ABD,

→tan30°= AB/BD

→1/√3 = h/(x+30)

✿From (1),we have

→h = x√3

◕Putting this value in(2) ,we get (x√3)√3=x+30

→3x=x+30

→3x-x=30

→2x=30

→x=30/2

→x=15

So,

→h= 15/√3

Therefore,the height of the tower is 15/√3m.