construct a triangle KMN with angle LMN= 60 degrees, MN = 9cm and LM 7cm. measure and state size of <MNL and on the diagram shwo the point K sucha that KLMN is a parralelogram
dont knw how to do it
In triangle LMN point L is at (-4,1). Where will L' be after a dilation with a scale factor of k = -3? *
To construct the triangle KMN, follow these steps:
1. Draw a line segment LM = 7 cm.
2. Extend the line segment LM to the right, creating a point N.
3. Using a compass, draw an arc with a radius of 9 cm from point M.
4. Label the intersection of the arc and the extended line segment as point N.
5. Draw a line segment MN connecting points M and N.
To find the measure of angle MNL, we know that angle LMN is already given as 60 degrees.
To find the measure of angle MNL, we need to subtract it from the sum of the other two angles in a triangle, which is 180 degrees.
angle MNL = 180 degrees - angle LMN - angle M = 180 degrees - 60 degrees - angle M
Now to find the value of angle M, we need to use the Law of Cosines.
The Law of Cosines states that for any triangle with side lengths a, b, and c and angle C opposite side c:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, angle M = angle MNL, side a = LM, side b = LN, and side c = MN.
Substituting the known values:
MN^2 = LM^2 + LN^2 - 2(LM)(LN) * cos(M)
Solving for cos(M):
cos(M) = (LM^2 + LN^2 - MN^2) / (2(LM)(LN))
Now we can use the given values to find cos(M), and then find angle M:
LM = 7 cm
LN = 9 cm
MN = 9 cm
Plug in the values:
cos(M) = (7^2 + 9^2 - 9^2) / (2(7)(9))
= (49 + 81 - 81) / (2(7)(9))
= 49 / 126
≈ 0.3889
Using the inverse cosine function (cos^(-1)), we can find the measure of angle M:
angle M ≈ cos^(-1)(0.3889)
≈ 67.19 degrees
Therefore, the measure of angle MNL is approximately 67.19 degrees.
To show that KLMN is a parallelogram, we need to draw a line segment KL parallel to MN and an equal distance from it.
1. Using a compass, set it to the length of MN, which is 9 cm.
2. Place the compass at point M and draw an arc intersecting line segment LN.
3. Place the compass at the intersection point and draw another arc above line segment MN.
4. Label the intersection of the second arc with the extended line segment LM as point K.
5. Draw a line segment KL connecting points K and L.
Now you have constructed the triangle KMN with angle LMN = 60 degrees, MN = 9 cm, and LM = 7 cm. The measure of angle MNL is approximately 67.19 degrees, and you have also shown that KLMN is a parallelogram by constructing a line segment KL parallel to MN.