Question

Trig problem i need help with

Answer 1

Answer:

Distance between boat and light house = 134 m

Step-by-step 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.

$\tan19\°=\frac{AB}{BC}$

Multiplying both sides by BC.

$BC\tan19\°=\frac{AB}{BC}\times BC$

$BC\tan19\°=AB$

Dividing both sides by tan 19°

$\frac{BC\tan19\°}{tan 19\°}=\frac{AB}{tan 19\°}$

$BC=\frac{AB}{tan 19\°}$

Substituting value of AB and tan 19°

$BC=\frac{46}{0.344}$

$BC=133.59\ m\approx134\ m$

Distance between boat and light house = 134 m