In sunlight, a vertical yardstick casts a 1 ft shadow at the same time that a nearby tree casts a 15 ft shadow. How tall is the

Question

Gnom [1K]

3 years ago

12

In sunlight, a vertical yardstick casts a 1 ft shadow at the same time that a nearby tree casts a 15 ft shadow. How tall is the

tree?

Mathematics

2 answers:

nadya68 [22] · Answer 1 · 2022-02-10T15:15:09+03:00

nadya68 [22]3 years ago

7 0

To answer this specific problem, the tree is 45 feet tall. I am hoping that this answer has satisfied your query and it will be able to help you, and if you would like, feel free to ask another question.

joja [24] · Answer 2 · 2022-02-10T17:39:26+03:00

Answer:

Tree is 45 ft tall.

Step-by-step explanation:

In the figure attached AB is the tree and CD is the yardstick.

Shadow of tree AB is BO = 15 ft and shadow of yardstick is CO.

since length of a yardstick is = 1 yard or 3 ft.

Now we know that ΔABO and ΔDCO are similar.(since ∠A = ∠D and ∠B = ∠C = 90° so AA property proving triangles similar)

Therefore $\frac{AB}{CD}=\frac{OB}{OC}$

By putting the values of AB and CD

$\frac{x}{3}=\frac{15}{1}$

x = 3×15 = 45 ft.

Therefore the height of the tree is 45 ft.