A triangle one angle measuring 3x degrees a second angle measures 2x+20 degrees and the third measures 4x-20 degrees. what is the value of x

x=20

Step-by-step explanation:

Because all angles of a triangle add up to 180, by adding all the values that your given and setting it equal to 180, you get the value of x.

3x+2x+20+4x-20=180

9x=180

x=20

In this right triangle  you know an angle and the adjacent leg, and need to find the opposite leg.

the formula that relates those three variables is:

tan(40°) = opposite leg / adjacent leg = height / 2 m

or, which is equivalent,  cot (40°) = adjacent leg / opposite leg = 2m / height

=> height = 2m / cot (40°).
which is the option c of the list.