Help! A tree casts a 20-foot shadow when the sun makes an angle of 42 degrees with the ground. Find the height of the tree to the nearest foot.

18.8 feet

Step-by-step explanation:

You have to use trigonometry for this question.

So, the basic measurements we have are:

1. The angle of elevation = 42 degrees

2. Base length of the triangle(ie. the shadow  on the floor) = 20 ft

Now, imagine a right angled triangle with the base length as the shadow height, the height of the triangle as the height of the tree and the hypotenuse as the sun ray that causes the shadow. Also, the angle opposite the height is the 42 degrees.

So, we know the Adjacent length and we want to know the opposite length ( in respects with the angle given)

So, the trig ratio that compares the two is ‘Tan’

Now, form the equation:

Tan (42) = Opposite/ Adjacent = O/ A = O/20

Rearrange to solve:

O/20 = Tan(42)

O = Tan(42) x 20

Key these into a calculator and you get the 18.800808...

Round to a suitable degree of accuracy.

18.8 ( 3s.f)

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

6x = 48

i hope this . 6 cards each and a total of $48. dvide each side by 6 and you will have your answer.