Precalculus- basics of trigonometry

[Jalen2418]

11. A biologist wants to know the width w of a river so that instruments for studying the pollutants in the water can be set properly. From point A the biologist walks downstream

feet and sights to point C (see figure). From this sighting, it is determined that θ = 54°. How wide is the river?

 

[HallsofIvy]

You titled this "basics of trigonometry"- do you know how the "tangent" function is defined? What is tan(54)?

 

[Jalen2418]

Yeah I had no idea what to put it under because I am taking precal its a subsection in my book though. Tan 54 is the outcome I believe of sine and cosine but I don"t know how to work backwards.

 

[Deleted member 4993]

11. A biologist wants to know the width w of a river so that instruments for studying the pollutants in the water can be set properly. From point A the biologist walks downstream

feet and sights to point C (see figure). From this sighting, it is determined that θ = 54°. How wide is the river?

Study the given figure with your problem.

Do you see a right-angled triangle?

What are the "height" and the "base" of that triangle?

Can you express tan54^o - in terms of those parameters shown in the given figure?

 

[Jalen2418]

I see what i need to do I just don't understand how to get x then after i find x I use Pythagorean theorem, but x is the part I am stuck on. Ohh by the way thanks for trying to help

 

[Steven G]

My goodness.

Tan(54) = w/140. Solve for w.

 

[HallsofIvy]

Yes, you know that, Subhotosh Kahn knows that, and I know that. We were were hoping that, with a little prodding, Jalen2418 would remember it!