If the distance from the boat to the lighthouse is 120 meters and the angle of elevation is 40°, which of the following equations will find the height of the lighthouse?

Question

icecreamsundae · Answer

attachment

Extrinix · Answer

Using the method of SOH CAH TOA, we can determine that the sign needed would be $\sf{tan}$.

Now, $\sf{tan}$ is opposite over adjacent (that’s where the “OA” of “TOA” comes from), so using this we can figure out what $\sf{tan(40)}$ equals.

(Provided in the image attached)

Extrinix · Answer

After all of this, we determine that the value that $\sf{tan}$ is equal to, is:

$\sf{tan(40) = \dfrac{120}{x}}$

(We do this by using the opposite over adjacent rule for $\sf{tan}$)

icecreamsundae · Answer

Ok so we use tan got it. and then would the equation be y/120?

Extrinix · Answer

Opposite over adjacent, close but not quite

icecreamsundae · Answer

oh man! Ok so the answer is tan(40)=120/x

icecreamsundae · Answer

Thank you for your help. @extrinix

Extrinix · Answer

@icecreamsundae wrote:

Thank you for your help. @extrinix

No problem!

1 attachment

1 attachment