Christa is standing on the top of head of gladwyn's shadow. If christa is 5 ft tall and Gladwyn's height is 6 feet and the length of their shadows combined is 15 ft, find the length of Christa's shadow
I see 2 similar triangles.
let length of Christa's shadow be x ft
let length of Glad's shadow be y ft
so 5/x = 6/y
6x = 5y
we also know x+y = 15
or y = 15-x
sub into the first:
6x = 5(15-x)
6x = 75-5x
11x = 75
x = 75/11 ft = appr 6.82 ft
y = 15-75/11 = 90/11 ft = appr 8.18 ft
To find the length of Christa's shadow, we will first calculate the length of Gladwyn's shadow. Since Christa and Gladwyn are standing in a straight line, their shadows will also be in a straight line.
Given that the length of their shadows combined is 15 feet, and knowing that Gladwyn's height is 6 feet, we can use proportionality to find the length of Gladwyn's shadow.
The proportion we can set up is:
(Length of Christa's shadow) / (Length of Gladwyn's shadow) = (Christa's height) / (Gladwyn's height)
Substituting the given values, we get:
x / (Gladwyn's shadow) = 5 / 6
To solve for x (Length of Christa's shadow), we can cross multiply:
6x = 5 * (Gladwyn's shadow)
Next, we substitute Gladwyn's shadow with the remaining length from the combined shadows:
6x = 5 * (15 - Christa's shadow)
Distributing 5 to both terms:
6x = 75 - 5 * Christa's shadow
Bringing all the terms containing Christa's shadow to one side:
6x + 5 * Christa's shadow = 75
Finally, we substitute the value of Christa's height (5 feet) to get:
6x + 5 * 5 = 75
Simplifying the equation:
6x + 25 = 75
Subtracting 25 from both sides:
6x = 50
Dividing by 6:
x = 50 / 6 = 8.33 (rounded to two decimal places)
Therefore, the length of Christa's shadow is approximately 8.33 feet.