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Vladimir [108]
3 years ago
12

Trig problem i need help with

Mathematics
1 answer:
zaharov [31]3 years ago
8 0

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

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