Given the triangle below, find sec X, tan X, and cos X in fraction form.
*right triangle, hypotenuse goes from top right to bottom left, bottom side is longer than top side. Top right point is z, left point is X, bottom right angle (the right angle) is Y. The short side, ZY=15, and the hypotenuse, XZ=25*
A. sec X= 5/3, tanX= 3/4, CosZ= 4/3
B. sec X= 5/4, tanX=3/4, cosZ= 3/5
C. sec X=4/3, tanX=3/4, cosZ= 5/3
D. sec X=5/4, tanX= 5/3, cosZ=4/5
Ok I'm thankful for the help but jeez you don't have to be like that. This is the second time you've done this. Maybe don't be a jerk about it?
Plus you didn't even answer it soooooo...
No, I didn't answer the question, but I gave you enough information so you could complete the solution.
Sorry to be jerk-ish.
To find sec X, tan X, and cos X in fraction form, we will use the given right triangle.
Let's start by identifying the sides of the triangle and their corresponding labels.
ZY represents the side opposite to X.
XZ represents the hypotenuse.
YZ represents the adjacent side to X.
Now, let's use the given information to calculate the values of sec X, tan X, and cos X.
Since sec X is the reciprocal of cos X, we can find cos X by dividing the length of the adjacent side by the length of the hypotenuse.
cos X = YZ / XZ = 15 / 25 = 3 / 5
Next, tan X is the ratio of the side opposite X to the adjacent side to X. Therefore, we can find tan X by dividing the length of the side opposite X by the length of the adjacent side.
tan X = ZY / YZ = 15 / YZ
To find YZ, we can use the Pythagorean Theorem, which states that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse.
YZ^2 + ZY^2 = XZ^2
YZ^2 = XZ^2 - ZY^2
YZ^2 = 25^2 - 15^2
YZ^2 = 625 - 225
YZ^2 = 400
Taking the square root of both sides, we get:
YZ = √400 = 20
Now, substitute the values into the equation for tan X:
tan X = 15 / YZ = 15 / 20 = 3 / 4
Finally, since sec X is the reciprocal of cos X, we can find sec X by taking the reciprocal of the fraction representing cos X:
sec X = 1 / cos X = 1 / (3 / 5) = 5 / 3
Therefore, the correct answer is:
A. sec X = 5/3, tan X = 3/4, cos Z = 4/3
So, with the triangle drawn as you have said, with the right angle on the x-axis, you just have a scaled up 3-4-5 triangle, with sides 15,20,25.
sinX = 15/25 = 3/5
cosX = 20/25 = 4/5
tanX = 15/20 = 3/4
Looks like time to review your basic trig functions and the Pythagorean Theorem.