Trig problem! (for burning man construction)?

Question

I have a trig problem that is going to go into a burning man project. It's a very important calculation so I need a second person to confirm my answer.

Have a 30 60 90 triangle. 2.6m side is adjacent to 30 deg and 90 deg angle. Need to find hyp. Thanks!

Answer 1

Let's take angle 30 to be our angle in question. That makes the opposite side and hypotenuse unknown. It makes the adjacent side equal to the hypotenuse.

Since we want hypotenuse, what we want is a relation between hypotenuse and adjacent. Adjacent and hypotenuse are related by cosine. Let's call the hypotenuse h.

cos(30) = adj/hyp = 2.6/h

Therefore,

h = 2.6/cos(30)

Fortunately, we know what cosine of 30 is. It's the same as the cosine of pi/6, which is sqrt(3)/2. So

h = (2.6) / [sqrt(3)/2]

We can change this into a simple fraction by multiplying top and bottom by 2.

h = (5.2) / sqrt(3)

We can even rationalize the denominator.

h = (5.2)sqrt(3) / 3

OR

h = (5.2)/3 sqrt(3)

Oh, for the heck of it, let's also change the fraction to integers.

h = (52/30) sqrt(3)
h = (26/15) sqrt(3)

That's the exact value of h, but if it's based on a real life project, you probably want an approximation.

h =~ 3.002

Answer 2

Ok, this is a right triangle problem...so we can apply our beloved Pythagoras theorem,

c^2 = a^2 + b^2

c^2 = 2(2.6)^2

taking the square root on both sides of the expression, you get,

c = 1.41(2.6)

c is aprox = 3.67

Good luck!

Answer 3

cos = adjacent side / hyp

so

hyp = 2.6 / cos(30) hyp = adjacent/ cos