Question

Three villagers A, B and C can see each other using telescope across a valley. The horizontal distance between A and B is 8 km and the horizontal distance between B and C is 12 km. The angle of depression of B from A is 20° and the angle of elevation of C from B is 30°. Calculate the vertical height between B and C. (tan 20° = 0.3640, `sqrt3` = 1.732)

Answer 1

Let AD is the vertical height between A and B

In the right ∆ABD

tan 20° = `"AD"/"BD"`

0.3640 = `"AD"/8`

AD = 0.3640 × 8 = 2.912 km

∴ AD = 2.91 km

CE is the vertical height between C and B

In the right ∆BCE, tan 30° = `"CE"/"BE"`

`1/sqrt(3) = "CE"/12`

⇒ `sqrt(3)"CE"` = 12

CE = `12/sqrt(3)`

= `(12 xx sqrt(3))/(sqrt(3) xx sqrt(3))`

= `(12 xx sqrt(3))/3`

= `4sqrt(3)`

= 4 × 1.732

= 6.928

= 6.93 km

The vertical height between B and C = 6.93 km