Question

Raul, who is 1.53 m tall, wishes to find the height of a tree. He walks 21.11 m from the base of the tree along the shadow of the tree until his head is in a position where the tip of his shadow exactly overlaps the end of the tree top's shadow. He is now 8.73 m from the end of the shadows. How tall is the tree?

Answer 1

Answer: 5.22m

Step-by-step explanation:

Using the rule of similar triangles where the the side lengths of two similar triangles are proportional

Parameters :

Tree height = t

Raul's height = 1.53m

Height of Raul's shadow = 8.73m

Total length of tree shadow = distance walked along tree shadow+ distance left to the end of tree shadow, Therefore,

Total length of tree shadow = 21.11 + 8.73 = 29.84m

Therefore,

Raul's ratio = tree's ratio

Raul's height : Raul's shadow = tree height : tree shadow

1.53 : 8.73 = t : 29.84

1.53/8.73 = t/29.84

1.53 × 29.84 = 8.73× t

t = 45.6552 / 8.73

t = 5.22m

Answer 2

Answer:

h = 5.23 m

Therefore, the tree is 5.23 m tall

Step-by-step explanation:

The question can be represented by the sketch in the attached image.

Where BE is the height of raul and CD is the tree's height (h)

Triangle ABE and ACD are both similar triangle.

And the ratio of their sides are equal

So,

BE/AE = CD/AD .....1

From the sketch,

BE = 1.53m

AE = 8.73m

CD = h

AD = 8.73 + 21.11m = 29.84m

Substituting into equation 1

1.53/8.73 = h/29.84

h = 29.84 × 1.53/8.73

h = 5.23 m

Therefore, the tree is 5.23 m tall