Question

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6m. At a point on the plane, the angle of elevation of the bottle and top of the flagstaff are 30° and 45° respectively. Find the height of tower. (Take √3 = 1.73)

Answer 1

Thus the height of the tower is h = 2.19 m

Step-by-step explanation:

h =  x tan (30°)          ----(1)

h + 6 = x tan (45°)         -----(2)

Now subtract equation (2) from (1).

6 =  x tan (45°) - x tan (30°)

6 = x (tan 45 - tan 30)

6 = x [1 - (-0.577)]

6 = x [1 + 0.577]

6 = 1.577 x

x = 6 / 1.577

x = 3.804

h = x tan 30

h = 3.804 x 0.577

h = 2.19 m

Thus the height of the tower is h = 2.19 m

Answer 2

Step-by-step explanation:

Tan 45°= (h+6)/x

1=(h+6)/x so x=h+6. EQ 1

Tan 30°=h/x

1/✓3=h/x

so x=✓3 h. EQ 2

putting the value of x in EQ 2