A student is standing 20 feet away from the base of a tree. He looks to the top of the tree at a 50 degree angle of elevation. His eyes are 5 feet above the ground. Using cos 50= .64, what is the height of the tree to the nearest foot?

23.84 feet

Step-by-step explanation:

Solving this question above, we using Trigonometric function tangent = Opposite/Adjacent

Opposite side + h = Height of the tree

We are told that:

A student is standing 20 feet away from the base of a tree. He looks to the top of the tree at a 50 degree angle of elevation. His eyes are 5 feet above the ground.

20 feet = Adjacent side = Distance form the tree

tan 50 = (h+5)/20

Cross Multiply

h + 5 = 20 × tan50

h = 20tan50 - 5

h= 18.835071852

h =18.84

Therefore the height of the tree is calculated as:

18.84+5 feet

=23.84 feet

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18