Exercise 23 Page 608

Let's draw a picture that describes the given situation, and we can add some characters to enhance our understanding. Let h be the height of a tree. We will rewrite Dave's height, 6 feet 4 inches, as a fraction 6 13 feet.

Since this is an example of a shadow problem, we can assume that the angles formed by the sun's rays with any two objects are congruent, and we can assume that the two vertical objects form the sides of two right triangles.

Since two pairs of angles are congruent, the above triangles are similar by the Angle-Angle Similarity Postulate. This means that the ratio of heights of these objects will be equal to the ratio of their shadow's lengths. h/6 13=66+ 15/15 We will now solve the above equation using cross multiplication.

h/6 13=66+15/15

AddTerms

Add terms

h/6 13=81/15

CrossMult

Cross multiply

h* 15=6 13*81

▼

Solve for h

MixedToFrac

a bc=a* c+b/c

h* 15=19/3*81

Multiply

Multiply

15h=19/3*81

MoveRightFacToNum

a/c* b = a* b/c

15h=19*81/3

Multiply

Multiply

15h=1539/3

CalcQuot

Calculate quotient

15h=513

DivEqn

.LHS /15.=.RHS /15.

h=513/15

CalcQuot

Calculate quotient

h=34.2

We found the height of the tree to be 34.2 feet. Thanks for the help Tall Dave!