Aflag post 10 meters long is fixed on top of a tower. from a point on horizontal ground, the angles of elevation of the top and bottom of the flag post are 40 degrees and 33 degrees respectively. calculate:
a) the height of the tower
b) the shortest distance from the point on the ground to the top of the flag post

Tan33=x/y

y= x/Tan33

Tan40=(10+x)/y

y= (10+x)/Tan40

Therefore

x/Tan33 = (10+x)/Tan40

xTan40-xTan33 =10Tan33

x= 10Tan33/(Tan40-Tan33)

x=34.2m

Step-by-step explanation:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

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step-by-step explanation:

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