Trigonometry Word Problem, Determining the Speed of a Boat, Example 3

[Xilosphere]

I'm relatively new to trigonometry, and I'm having difficulty understanding where values like 2.14 are coming from... I already know about Sin/Cos/Tan = Soh/Cah/Toa, but it's as if I'm missing something between finding some angle theta, and deriving calculations from specific degrees (e.g. 65°).

Furthermore, how does Sine/Tan differ from Cosine/Cotangent? What about Secant/Cosecant? I think I'm just lost with how this all works because I'm not seeing the specific values of trigonometric identities. In the way that Pi = 3.14159... Instead it seems numbers are "just appearing" after identities get submitted into a calculator.

[georgied]

im confused why change the tan65 to a decimal answer its different? when i put in 800/tan65 it equals 373.05 and yours by changing the tan65 is 373.83. If im doing problems should i change the tan65 bit to a number will this help ? great problem but just not sure

[cherryvanilla]

do you have any more examples like this?

[yarhannaariza]

A lighthouse at sea level is 34 mi from a boat. It is known that the top of the lighthouse is 42:5 mi from the boat and that x=rcose, where x is the horizontal distance, r is the distance of the top of the lighthouse from the boat, and is the angle of depression from the top of lighthouse. Find 0

Can you answer this?

[BillyBooful]

This would be a lot of help if I wasn't Australian... This American feet and miles is too weird! o.O

[MikeRichards]

just pretend he is using km it doesn't really make a difference

[mukhtiarahmed]

It is not easy to understand, as a leftest way to determining.