in a triangle xyz,if xy =120m,yz=100m and xz=180m make a scale drawing of the triangle and find the value of angle x.Note:for the sake of your sheet,use 1cm to represent 40m
I will assume that this is a right triangle
Cannot draw on these posts.
wdym
using Law of Cosines
yz^2 = xy^2 + xz^2 - [2 * xy * xz * cos(x)]
To make a scale drawing of the triangle XYZ, we can use the given scale of 1cm to represent 40m.
Step 1: Determine the lengths of the sides in the scale drawing.
- On the scale drawing, mark a line segment for XY. Since XY is 120m, we need to represent this on the scale drawing. Since 1cm represents 40m, we can find the length on the scale drawing by dividing 120m by 40: 120m / 40m = 3cm.
- Mark a line segment for YZ. Since YZ is 100m, on the scale drawing this will be: 100m / 40m = 2.5cm.
- Mark a line segment for XZ. Using the same scale, XZ will be: 180m / 40m = 4.5cm.
Step 2: Draw the triangle.
- Start by drawing XY. Since XY is 3cm on the scale drawing, draw a line segment that is 3cm in length.
- From the endpoint of XY, draw YZ, which is 2.5cm on the scale drawing. Connect the endpoint of YZ back to X, forming the triangle XYZ.
- Make sure all sides are connected and the angles are approximately correct.
Step 3: Find the value of angle X.
To find the value of angle X, we can use the Law of Cosines. The Law of Cosines states that in a triangle ABC, where sides a, b, and c correspond to angles A, B, and C respectively:
c^2 = a^2 + b^2 - 2ab * cos(C)
Let's apply this to triangle XYZ and find angle X.
- Let xy = 120m, yz = 100m, and xz = 180m, as given in the problem.
- We need to find angle X, which corresponds to side XY.
- Applying the Law of Cosines, we have:
(120m)^2 = (100m)^2 + (180m)^2 - 2(100m)(180m) * cos(X)
Simplifying this equation, we get:
14400 = 10000 + 32400 - 36000 * cos(X)
Simplifying further, we have:
3600 = 68400 - 36000 * cos(X)
Rearranging the equation, we get:
36000 * cos(X) = 68400 - 3600
36000 * cos(X) = 64800
cos(X) = 64800 / 36000
cos(X) = 1.8
Taking the inverse cosine of both sides to find angle X, we get:
X = cos^(-1)(1.8)
However, the value of 1.8 is greater than the range of the cosine function (-1 to 1), so angle X in this triangle cannot be found.