To find the length of side MK (x), we use the cosine of angle LKM which is 49 degrees, with LK given as 20 units. Calculating 20 × cos(49°) gives us the length of MK, which is approximately 13.12 units.
To solve for x in the right angle triangle KLM, where angle KLM is 90 degrees and angle LKM is 49 degrees, and LK (the opposite side to angle LKM) equals 20, you can use trigonometric ratios.
Since angle LKM is given and adjacent side MK is denoted as x, we'll use the cosine function:
cos(LKM) = adjacent/hypotenuse
cos(49°) = x/LK
cos(49°) = x/20
Now, compute the cosine of 49 degrees and multiply both sides by 20 to solve for x:
x = 20 × cos(49°)
Using a calculator, find x:
x = 20 × 0.6561 (cosine of 49° approximately)
x = 13.12
Therefore, MK is approximately 13.12 units long.
The probable question may be:
In a geometry problem in the USA curriculum, angles are represented as follows: ∠LLF = 53°, ∠G = 45°, and ∠H is unknown. If x represents the measure of ∠H, what is the value of x in degrees?