Answer:
x = 27
Step-by-step explanation:
Based on the angle bisector theorem, we would have the following:
(x + 8)/10 = (2x - 5)/14
Cross multiply
14(x + 8) = 10(2x - 5)
14x + 112 = 20x - 50
Collect like terms
14x - 20x = -112 - 50
-6x = -162
Divide both sides by -6
-6x/-6 = -162/-6
x = 27
Answer: The height is 6.07 meters
Step-by-step Explanation: The distance between the elevator and the bottom of the barn is given as 9 meters. Also for the hay elevator to move bales of hay to the second story of the barn lift it makes an angle of elevation of 34 degrees with the ground. With these we can derive a right angled triangle with the reference angle as 34 degrees, the side facing it which is the height or h (opposite) is yet unknown, and the side between the reference angle and the right angle (adjacent) is 9. We shall apply the trigonometric ratio as follows;
Tan 34 = opposite/adjacent
Tan 34 = h/9
0.6745 = h/9
0.6745 x 9 = h
6.0705 = h
Therefore the approximate height of the barn to the ground is 6.07 meters
Step-by-step explanation:
factor 4 out of the variable terms, as this helps.
but my approach is simply to define the target and then calculate "backwards".
we want to find
(ax + b)² = a²x² + 2abx + b²
and now we compare with the original equation :
a²x² = 4x²
a² = 4
a = 2
2abx = 16x
2×2×bx = 16x
4b = 16
b = 4
b² = 16, but we have only 3, so we need to subtract 16-3 = 13 from the completed square.
so, our equation is
(2x + 4)² - 13 = 0
(2x + 4)² = 13
2x + 4 = sqrt(13)
2x = sqrt(13) - 4
x = sqrt(13)/2 - 2
