The angle of elevation of the sun from the ground to the top of a tree is 36 degrees
<h3><u>Solution:</u></h3>
Given that a tree that is 10 yards tall cast a shadow 14 yards long
To find: angle of elevation of sun
The figure is attached below
In the figure, AB represents the height of tree
BC represents the length of shadow cast by tree
We have to find angle of elevation θ
Now by using trignometric identity,
From the figure,
AB = Perpendicular = 10 yards
BC = Base = 14 yards
Thus the angle of elevation of sun from ground to top of tree is 36 degrees
Two consecutive integers can be written like x, and x+1
sum means add them together.
so,
combine like terms and solve for x.
Exactly what is your question?
Answer:
x = 16
Explanations:
Since △ACD ~ △ABE, it means that:
CD/AD = BE/AE..........(*)
CD = 3x + 8
AD = AE + ED
AD = (x - 1) + 27
AD = x + 26
BE = 20
AE = x - 1
Substituting CD, AD, BE, and AE into equation (*)
(3x+8)/(x+26) = 20/x-1
Cross multiply:
(3x+8)(x-1) = 20(x+26)
3x² - 3x + 8x - 8= 20x + 520
3x²- 15x - 528 = 0
Divide through by 3
x² - 5x - 176 = 0
Solving the quadratic equation above for the values of x
x² - 16x + 11x - 176 = 0
x(x - 16) + 11 (x - 16) = 0
(x - 16)(x + 11) = 0
If x - 16 = 0
x = 16
If x + 11 = 0
x = -11
x cannot be -11 because x = -11 will make side CD and AE to be negative, and the sides of a triangle cannot be negative.
Therefore, x = 16
Answer:
16
Step-by-step explanation:
took test