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`40sqrt3` m`30sqrt3` m`20sqrt3` m`10sqrt3` m

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ASolution :

For the maximum possible distane, two points lie on either side of the tower. <br> Let AB be the height of the tower. <br> AB = 30 m (given) <br> Let P and Q be the given points <br> In `DeltaABP`, <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/PS_MATH_X_C08_E06_015_S01.png" width="80%"><br> `tan30^(@)=(AB)/(PB)rArr(1)/(sqrt3)=(30)/(PB)rArrPB=30sqrt3`. <br> `In DeltaABQ, tan60^(@)=(AB)/(BQ)` <br> `rArrsqrt3=(30)/(BQ)rArrBQ=(30)/(sqrt3)`m. <br> Now, PQ =PB+BQ <br> `=30sqrt3+(30)/(sqrt3)=30(sqrt3+(1)/(sqrt3))` <br> `30((4)/(sqrt3))=40sqrt3` m. **Application of trignometry in real life.**

**Explain the angle of elevation & depression with the help of diagram.**

**A circus artist is climbing a 20 m long rope ; which is tightly stretched and tied from the top of a vertical pole to the ground . Find the height of the pole if the angle made by the rope with the ground level is `30^@`**

**From the top of the hill; the angle of depressions of two consecutive kilometre stones due east are found to be `30^@` and `45^@` . Find the height of the hill.**

**The shadow of a flag staff is 3 times as long as shadow of the flag-staff when the sunrays meet the ground at an angle of `60^@`. Find the angle between the sun rays and the ground at the time of longer shadow.**

**The angle of elevation of a cloud from a point 60m above a lake is `30^@` and the angle of depression of the reflection of cloud in the lake is `60^@`. Find the height of the cloud.**

**From the top of a building 15m high the angle of elevation of the top of tower is found to be `30^@`. From the bottom of same building ; the angle of elevation of the top of the tower is found to be `60^@`. Find the height of the tower and the distance between tower and building .**

**A man on a cliff observes a boat at an angle of depression of `30^@` which is approaching the shore to the point immediately beneath the observer with a uniform speed . Six minutes later ; the angle of depressions of the boat is found to be `60^@`. Find the time taken by boat to reach the shore.**

**The elevation of a tower at a Station A due north of it is `alpha` and at a station B due west of A is `beta`. Prove that the height of the tower is `(ABsinalphasinbeta)/sqrt(sin^alpha-sin^beta)`**