Question

From the top of a church spire 96 m high, the angles of depression of t:vo
vehicles on a road, at the same level as the base of the spire and on he
same side of it are rº and yº, where tanto and tan jo
4
Calculate the distance between the vehicles.​

Answer 1

Answer:

From the top of a church spire 96 m high, the angles of depression of t:vo

vehicles on a road, at the same level as the base of the spire and on he

same side of it are rº and yº, where tanto and tan jo

4

Calculate the distance between the vehicles.

Answer 2

We are given that from the top of tower 96m high, the angles of depression of two cars on a road at the same level as the base of the tower and on the same side of it are theta and phi, where tan theta =3/4 and tan phi = 1/3.

In the figure drawn below; let \angle ACB = \text{tan} \theta = \frac{3}{4}  and  \angle ADB = \text{tan } \phi = \frac{1}{3} and also the height of the tower = AB = 96 m.

Now, as we know that \text{tan } \theta = \frac{\text{Perpendicular}}{\text{Base}}

So, in \triangleABC,

\text{tan } \theta = \frac{AB}{BC}

\frac{3}{4 } =\frac{96}{BC}

BC = \frac{96 \times 4}{3}

BC = 32 \times 4 = 128 m

Now, in \triangleABD,

\text{tan } \phi = \frac{AB}{BD}

\frac{1}{3} =\frac{96}{BD}

BD = \frac{96 \times 3}{1}

BD = 288 m

So, the distance between two cars = CD = BD - BC

                                                                   = 288 m - 128 m = 160 m.