Question

Trig problem i need help with

Answer 1

Distance between boat and light house = 134 m

Explanation:

Given data:

Height of light house = 46 m

Angle of elevation from boat to the top of light house = 19°

From the data given to us we can construct a right triangle ABC.

For the Δ ABC

AB= 46 m

∠C= 19°

We can apply trigonometric ratio to find side BC which is the distance of light house from the boat.

`\tan19\°=(AB)/(BC)`

Multiplying both sides by BC.

`BC\tan19\°=(AB)/(BC)* BC`

`BC\tan19\°=AB`

Dividing both sides by tan 19°

`(BC\tan19\°)/(tan 19\°)=(AB)/(tan 19\°)`

`BC=(AB)/(tan 19\°)`

Substituting value of AB and tan 19°

`BC=(46)/(0.344)`

`BC=133.59\ m\approx134\ m`

Distance between boat and light house = 134 m