Question

Two points A and B are on the same side of the tower and in the same stright line witb its base .The angle of desperation of these points are the top of the tower are60 degree and 45 degree . if the height if the tower is 1.5cm .then find the distant between these point

Answer 1

i guess this would help....

Answer 2

Answer:

0.63 cm

Step-by-step explanation:

Refer the attached figure .

Height of tower i.e. DC = 1.5 cm

Angle of depression at A i.e. ∠DAC= 60°

Angle of depression at B i.e. ∠DBC= 45°

In ΔDCA

DC = perpendicular

AC = base

using trigonometric ratio

$tan\theta = \frac{perpendicular}{base}$

$tan60^{\circ} = \frac{DC}{CA}$

$\sqrt{3}= \frac{1.5}{CA}$

$CA= \frac{1.5}{\sqrt{3}}$

In ΔDBC

DC = perpendicular

BC = base

using trigonometric ratio

$tan\theta = \frac{perpendicular}{base}$

$tan45^{\circ} = \frac{DC}{BC}$

$1= \frac{1.5}{BC}$

$BC = 1.5$

Since the distance between A and B = BC - AC = $1.5- \frac{1.5}{\sqrt{3}}$

BC -AC = 0.63

Thus the distance between A and B is 0.63 cm