If cot x° = three fourths, what is the value of b? triangle LMN in which angle M measures 90 degrees, angle L measures x degrees, LM measures 10.5 units, and NM measures 2b units

The value of b is 4.

Step-by-step explanation:

The value of b which is half the length of the side NM is 7 units.

Step-by-step explanation:

To solve the question, we note that it is a triangle trigonometry question. Therefore, we proceed as follows;

Since cot x = 3/4, then tan x = 4/3 and x = tan⁻¹(4/3) = 53.13 °

Therefore we have triangle LMN with M = 90 °

L = x = 53.13 °

Side LM = 10.5 units

Side NM = 2b units

But tan L = NM/LM  = 2b/10.5

Angle L is known as 53.13 and tan x = tan L = 4/3

Therefore, 4/3 = 2b/10.5

and 2b = 10.5×4/3 = 14

b = 7 units