A tree is 40 feet tall and casts a shadow of 30 feet, to the nearest degree, what is the angle of elevation from the ground to the top of the tree?

The angle of elevation is adjacent to the right angle of a triangle; therefore, the angle of elevation here is x degrees.

To find an unknown angle, we first have to set up a trigonometric ratio. In the diagram provided we are given the adjacent and opposite sides, so we will use tangent.

tan x: opposite/adjacent

tan x: 40/30

tan x: 1.33333333

Now to find the angle measure, use and calculate the inverse of tan. 1.33333333.

x = tan^-1 (1.33333333)

x = 53.130102 or 53 degrees rounded to the nearest degree

To check our work we can use the Triangle Sum Theorem:

53+90+x=180

143+x=180

143-143+x=180-143

x=37

37+53+90=180

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation:

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.