Construct a triangle KLM,if kl=8cm,lm=10cm and km=6cm.measure the largest angle of the triangle.
Straight line will meet at a point
To find the largest angle of a triangle, we can use the Law of Cosines. Let's label the largest angle as angle K.
According to the Law of Cosines, we have the formula:
c^2 = a^2 + b^2 - 2ab * cos(C)
Where:
- c is the side across from angle C
- a and b are the other two sides
- C is the angle opposite to side c
In our case, side c is KL, side a is LM, and side b is KM.
Using these values, we can rearrange the formula to solve for the cosine of angle K:
cos(K) = (LM^2 + KM^2 - KL^2) / (2 * LM * KM)
Plugging in the values from the given measurements, we get:
cos(K) = (10^2 + 6^2 - 8^2) / (2 * 10 * 6)
= (100 + 36 - 64) / 120
= 0.6
To find the measure of angle K, we need to find the arccosine (inverse cosine) of 0.6. Using a calculator or a table of trigonometric values, we find:
K ≈ 53.13 degrees
Therefore, the largest angle of the triangle KLM is approximately 53.13 degrees.