Angle of ElevationAngle of Elevation

Angle of Depression

Ex. # 11.2

Q. 1Q. 4Q.16

Angle of ElevationAngle of Elevation

A

B

The Object observed from the point of observation in UPWARD direction makes an angle of Elevation. /ACB is an angle of Elevation of Object B

While flying a kite your kite makes an angle of elevation at the point where you stand.

Example :-

Point of Observation

C

Angle of DepressionAngle of Depression

Point of Observation

AA

BB

Angle of Depression is formed by observing an object B from HIGHER level to LOWER level. /ACB is an angle of Depression of Point B.

Example:-

While flying a fighter, pilot hits the target by checking the angle of Depression of the target.

CC

Exercise 11.2

1. Measure of the angle of elevation of the top of a flagstaff observed from a point 200 meters from its foot is 30o.

Find its Heights.

30o H=?

Solution:-

200m

Let Height of Flagstaff be H = ?

=115.47 m Ans.

H = 200 x tan30o

tan30o = H / 200

From Fig. We have

Q. 4. The Measure of the angle of elevation of the top of a tower is 67o. What is the measure of elevation of point 2/3 way up the tower from the same point where an observer stands.

67o67o

h

h2/3

??

Click to See Solution On Next Page:

= 57.25o Ans. = 57.25o Ans.

Solution : Ex. # 11.2 (4)

AA

BB

CC

h

(2/3)h

?o67o

Tan 67o = h/d …………… (1)Tan 67o = h/d …………… (1)

Tanx = (2/3)h/d ……………. (2)Tanx = (2/3)h/d ……………. (2)

Put the value of h/d from (1) in (2) We get Put the value of h/d from (1) in (2) We get

Tanx = (2/3)tan67oTanx = (2/3)tan67o

= 1.55= 1.55

x = tan-1 1.5x = tan-1 1.5

In Triangle ABC In Triangle ABC

In Triangle ADCIn Triangle ADC

DD

Q.16 From the top of a hill 2000 meters high the measure of he angle of depression of a point on the nearer shore of a river is 70o and the measure of angle of depression of a point directly across the river is 50o. Find the width of the river. How far is the river from the foot of the hill ?

70o70o

70o70o

50o50o

50o50o

Width Of River ?Width Of River ?

2000m2000m

Distance of River from Cliff ?

Distance of River from Cliff ?

Solution:

In fig we haveIn fig we have

Tan70o = h / x2Tan70o = h / x2

Tan70o = 2000 / x2……………………(1)Tan70o = 2000 / x2……………………(1)

x2 = 2000/ Tan70o = 727.94mx2 = 2000/ Tan70o = 727.94m

Dis. Of Hill from River = 727.94m Ans.Dis. Of Hill from River = 727.94m Ans.

Now we take Now we take

Tan50o = h / ( x1 + x2 )Tan50o = h / ( x1 + x2 )

Tan50o = 2000 / ( x1 + 727.94 )Tan50o = 2000 / ( x1 + 727.94 )

( x1 +727.94 ) Tan50o =2000( x1 +727.94 ) Tan50o =2000

( x1 +727.94 ) =2000/ Tan50o( x1 +727.94 ) =2000/ Tan50o

x1 + 727.94 = 1678.19x1 + 727.94 = 1678.19

x1 = 1678.19 - 727.94x1 = 1678.19 - 727.94

Width of River = 950.24m Ans.Width of River = 950.24m Ans.

70o70o

70o70o

50o50o

50o50o

X1X1 x2 ?x2 ?

h=2000mh=2000m