Trig Problem: find lengths of e and f w/o calculator

[snakeyesxlaw]

A = 60 degrees
d = 150 ft

solve the length for e and f (no calculators)?

okay, so 50 degrees multiplied by (pi / 180 degrees) = 5pi/18

A = 5pi /18

B = pi / 2

C = (pi / 2) - (5pi / 18) = 2pi / 9

so how do i go about in getting the length of the sides?

 

[stapel]

Draw an equilateral triangle with side-length 2. (Yes, I know that's not what you're working with here. Bear with me....)

From the peak, draw the vertical "altitude" line, bisecting the triangle.

The original triangle obviously had all three angles being sixty degrees. The vertical line meets the base at a right angle, and bisects the angle at the peak.

Look at one of the half-triangles. This is a 30-60-90 triangle. The hypotenuse has length 2. The short side has length 1. Use the Pythagorean Theorem to find the length (in "exact" radical form) of the long side.

This gives you the ratio of sides for any 30-60-90 triangle. In your particular triangle, the angle at A is sixty degrees. Compare this triangle to your labelled half-triangle, and find the corresponding parts:

The hypotenuse should be twice the length of the base. The long side should be (the radical you found) times the length of the base.

I'll bet you can do it now! :wink:

Eliz.

 

[snakeyesxlaw]

actually, i made a mistake.. that should be 50 degrees and not 60 degrees..

so am guessing to solve for one of the sides, we would leave the expression with a trig function still in it? since its not a 30-60-90 or a 45-45-90..

 

[snakeyesxlaw]

actually figured it out.. it turned out to be a matter of leaving the answer in trig equation form as the exact answer..

 

[jwpaine]

Cos(pi/3) = adj / hyp = d / f = 150 / f
Cos(pi/3) = 150 / f
f = 150Cos(pi/3) = 150(1/2) = 75

Now use Pythagoras to find e.

John

 

[snakeyesxlaw]

Cos(pi/3) = adj / hyp = d / f = 150 / f
Cos(pi/3) = 150 / f
f = 150Cos(pi/3) = 150(1/2) = 75

Now use Pythagoras to find e.

John

wrong.. where'd u get pi/3? the angles are pi/2, 5pi/18, and 2pi/9

it was actually leaving it like:

f = 150 ft / cos50

simplistic, cause there is no other way to solve any further without using a calculator based on the information provided.

 

[o_O]

He probably got pi/3 since you said A = 60 until you changed it later in your post.

And yes that would be correct for f unless you really wanted to find an equivvalent expression to cos50.