In a 30-60-90 triangle, the length of the side opposite the 30 degree angle is 8. Find the length of the side opposite the 60 degree angle.

The length of the side opposite the 60 degree angle 'c' = 4

Step-by-step explanation:

Step(i):-

Given data ∠A = 90° , ∠B = 60° and ∠C = 30°

Given data the length of the side opposite the 30 degree angle is 8

let  'a' = 8

step(ii):-

By using sine rule formula in properties of triangle

cross multiplication , we get

we know that trigonometry formulas

sin 30° =   and sin 90°= 1

C =  8 X 1/2 = 4

conclusion:-

The length of the side opposite the 60 degree angle 'c' = 4

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.