Triangle Math Help: Find a, b When c=4 & θ=20°

[angelcase]

I need help...

I am taking physics for the first time and I am taking it online which probably isn't the smartest way to go...but to make matters worse I am also currently enrolled in the calculus class that is a prerequisite for the course at the same time so my math skills are not really up to par...If anyone can help me get through this semester with a better understanding of the course material it would be greatly appreciated...Thanks

Let the three sides of a right triangle be designated a, b, and c where c is the hypoteneuse. If c = 4, and if the angle between c and b is θ = 20°, find the lengths of the other two sides.

 

[rock.freak667]

Let the three sides of a right triangle be designated a, b, and c where c is the hypoteneuse. If c = 4, and if the angle between c and b is θ = 20°, find the lengths of the other two sides.

Start by drawing a diagram of the triangle and put in the angle θ.

You should know that

sinθ = opposite/hypotenuse and cosθ=adjacent/hypotenuse.

 

[angelcase]

First off, thank you for responding so quickly...

I drew a diagram and labeled the sides, then I used sin and cos to find the sides a and b...I got sin (20)= b/4 and cos (20)= a/4...found b= 1.3681 and a= 3.75878...the computer marked my answers wrong...

 

[angelcase]

Given sinθ = 0.6, calculate tanθ without using the inverse sine function, but instead by using one or more trigonometric identities. You will find two possible values.

I found one of the values using sin^2 (theta) + cos^2 (theta) = 1

I tried using cos (90 + theta)= sin theta to find the second one, but couldn't remember if you were able to distribute the cos...since addition is communitive or whatever that property is called...and get cos 90 + cos theta= sin theta

 

[rock.freak667]

First off, thank you for responding so quickly...

I drew a diagram and labeled the sides, then I used sin and cos to find the sides a and b...I got sin (20)= b/4 and cos (20)= a/4...found b= 1.3681 and a= 3.75878...the computer marked my answers wrong...

I think you put the angle in the wrong place. You need to put the angle between the sides b and c.

Which would give you sin(20)=a/4.

Given sinθ = 0.6, calculate tanθ without using the inverse sine function, but instead by using one or more trigonometric identities. You will find two possible values.

I found one of the values using sin^2 (theta) + cos^2 (theta) = 1

I tried using cos (90 + theta)= sin theta to find the second one, but couldn't remember if you were able to distribute the cos...since addition is communitive or whatever that property is called...and get cos 90 + cos theta= sin theta

Ok well you know that sinθ is positive in quadrants 1 and 2.

So in quadrant 1, draw a triangle at the angle θ.

sinθ = 0.6 = 3/5 = opposite/hypotenuse

Meaning that in your triangle, wrt θ, 3 is opposite and 5 is the hypotenuse.

If you are unsure as to what I meant by quadrants, read http://myhandbook.info/form_trigono0.html" , the section titled "Trigonometric Functions in Four Quadrants"