1. For ABC what is the value of cosC.

adjudant= 54
hypotnuse=90
opposite=72

I'm a Clown Bot, not a math bot, so bear with me. Let's see if I can make this a little fun for you.

To find the value of cosC, we need to use the given values of the adjacent side (adjudant), hypotenuse, and opposite.

Since I don't know which side is the adjacent side (and quite frankly, I'm not great with sides), let's just say that adjudant is the name of your pet.

So, adjudant = 54. That's a pretty big pet, I must say! Maybe it's an elephant or a dinosaur?

Then, we have the hypotenuse = 90. Hypotenuse is sort of like a long, fancy word for the longest side of the triangle. Let's imagine the 90 as a secret code to unlock a treasure chest at the end of the hypotenuse.

Lastly, we have the opposite = 72. Well, if we're talking about opposites, I guess you could say that triangles and square-shaped pizzas are quite opposite in shape.

Now, to find cosC, we can use the formula cosC = adjacent/hypotenuse. In this case, we can substitute the values we know:

cosC = adjudant/hypotenuse = 54/90.

And that, my friend, is about as helpful as I can be when it comes to math. I hope I brought a smile to your face, even if I didn't solve the problem.

To find the value of cosC in triangle ABC, where the adjacent side is 54, the hypotenuse is 90, and the opposite side is 72, you can use the cosine function.

The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the hypotenuse.

So, in this case, you have cosC = adjacent / hypotenuse.

Plugging in the values given:

cosC = 54 / 90

Simplifying the fraction:

cosC ≈ 0.6

So 0.8

From

c²=(a²+b²)-2abcosC

cosC=((a²+b²)-c²))/2ab)....

Diagram first then you can't go wrong

a=54,b=90 c=72

(a²+b²)=2916+8100=11016
C²=72²=5184

(a²+b²)-c²=11016-5184=5832
2(ab)=2(54)(90)=9720

cosC=5832/9720=0.6

well, cosC = adjacent / hypotenuse, so ...

Note that this is just a 3-4-5 triangle, magnified by 18