Question

A vertical pole BP stands at one corner of a horizontal rectangular field as shown.
If AB= 10m, AD= 5m and the angle of elevation of P from A is 22 degrees, calculate:
a) the height of the pole
b) the angle of elevation of P from C
c) the length of a diagonal of the rectangle ABCD
d) the angle of elevation of P from D

Answer 1

Answer:

Step-by-step explanation:

a) tan22 = BP / 10m

tan22 (10m) =BP

b) BP/5m = tanC

c)

(102)+(52)−−−−−−−−−−√=diagonaloftherectangle

Answer 2

Given :  A vertical pole BP stands at one corner of a horizontal rectangular field as shown.  If AB= 10m, AD= 5m and the angle of elevation of P from A is 22 degrees,

To find : a) the height of the pole

b) the angle of elevation of P from C

c) the length of a diagonal of the rectangle ABCD

d) the angle of elevation of P from D

Solution:

AB = 10 m  

AD = 5  m => BC = 5 m

rectangular field

=> BD² = AB² + AD²

=> BD² = 10² + 5²

=> BD² = 100 + 25

=> BD² = 125

=> BD = 5√5  m

the length of a diagonal of the rectangle ABCD =  5√5  m  = 11.2m

angle of elevation of P from A is 22 degrees,

=> Tan 22   =  BP / AB  

=> 0.4  = BP/10

=> BP = 4  m

Height of pole = 4  m

the angle of elevation of P from C

=> Tan ( angle)  = BP/BC

=>  Tan ( angle)  = 4/5

=>   Tan ( angle)  = 0.8

=> angle of elevation of P from C = 39°

the angle of elevation of P from D

=> Tan ( angle)  = BP/BD

=>  Tan ( angle)  = 4/11.2

=>   Tan ( angle)  = 0.36

=> angle of elevation of P from D = 19.8°  

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