# Coordinates of third point in a triangle for a program (sorry in advance for my english, i'm french) I'm in high school and i'm trying to do a program on python and i need to find the coordinates...

Coordinates of third point in a triangle for a program

(sorry in advance for my english, i'm french) I'm in high school and i'm trying to do a program on python and i need to find the coordinates of a third point C knowing : ABC is right-angled in C, angle(ABC)=16 degree, AB = 24 and i know the coordinates of A and B Thanks in advances ! (can you just please make it easy to understand ? I'm still only in high school...)

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### 1 Answer

At enotes, educators do not write programs for a student, that is, finish up their assignment. However, the educators provide enough information to guide the student along the correct path. So within those bounds, I will help you in finding the coordinates of the third point, C, given the other information.

Given information:

ABC is a right angled triangle in C.

`/_` ABC = 16 degrees, therefore, `/_` CAB = 90-16 = 74 degrees

AB = 24 units

Coordinates of A and B are known. Let these be (xa, ya) and (xb, yb).

Using trigonometry,

cos (`/_` ABC) = cos (16) = BC/AC = BC/24

Therefore, BC = cos (16) x 24 = 0.961 x 24 = 23.07 units.

Similarly, sin (`/_` ABC) = sin (16) = AC/AB = AC/24

Therefore, AC = 24 x sin (16) = 0.407 x 24 = 9.76 units

Now, the distance between any two points can be calculated by knowing the coordinates of the two. We will use the same identity, given the coordinates of A and B; and assuming the coordinates of C as (xc, yc).

Therefore, AC^2= (xa-xc)^2 + (ya-yc)^2

similarly, BC^2 = (xb-xc)^2 + (yb-yc)^2

Since, the coordinates of A (xa, ya)) and B (xb, yb) are given and we have already calculated AC and BC, we can use all the given information in conjunction with the above equations to solve for xc and yc and thus obtain the coordinates of point C.

Hope this helps.