Respuesta :
Answer:
17 feets 3 inches
Step-by-step explanation:
Given :
Converting the parameters to inches only:
Recall:
1 feets = 12 inches
Man's height : 5 feets 9 inches = (12 *5) + 9 = 69 inches
Man's shadow : 3 feets 6 inches = (12 * 3) + 6 = 42 inches
Tree's shadow : 10 feets 6 inches = (12 * 10) + 6 = 126 inches
(Tree's height / tree's shadow) = (man's height / man's shadow)
Let tree's height = x
x / 126 = 69 / 42
Solve for x
42x = 126 * 69
42x = 8694
x = 8694 / 42
x = 207 inches
207 / 12 = 17 feets 3 inches
Answer:
17.25 ft
Step-by-step explanation:
The figure shows two triangles X Y Z and H R Q. Side X Y has a length of h units, side Y Z has a length of 10 feet 6 inches, angle Y is a right angle. Side H R has a length of 5 feet 9 inches, side R Q has a length of 3 feet 6 inches. Angle R is a right angle.
Let h be the height of the tree.
Convert all measurements to a single unit, inches, using the fact that 1 foot is equal to 12 inches.
ZY=(10⋅12) in.+6 in.
Simplify.
ZY=126 in.
QR=(3⋅12) in.+6 in.
Simplify.
QR=42 in.
HR=(5⋅12) in.+9 in.
Simplify.
HR=69 in.
ZX¯¯¯¯¯ and QH¯¯¯¯¯¯ are parallel because the rays of the Sun that form them are parallel. Therefore, the angles they form with the ground are congruent: ∠Z≅∠Q.
∠Y≅∠R by the Right Angle Congruence Theorem.
Therefore, by the Angle-Angle Similarity △ZXY~△QHR.
Find XY. Set up a proportion with the lengths of the known sides and the unknown length (height of the tree).
ZY/QR = XY/HR
Substitute the values.
126/42=h/69
Cross multiply.
42h=69(126)
Simplify.
42h=8694
Divide both sides by 42.
h=207 in.
Therefore, the height of the tree is 207 in., or 17.25 ft.
