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Rina8888 [55]
3 years ago
11

the height of an object varies directly with the length of its shadow. a person 6ft tall casts a 8.5ft shadow, while a tree cast

s a 38ft shadow. how tall is the tree
Mathematics
1 answer:
mixer [17]3 years ago
5 0

Answer:

The answer to your question is   Tree's height = 26.8 ft  

Step-by-step explanation:

Data

Person                         Tree

height = 6 ft                 height = x

shadow = 8.5 ft            shadow = 38 ft

Process

1.- Use the Thales' theorem to solve this problem

   Person's height/ Person's shadow = Tree´s height / Tree's shadow

Solve for Tree's height

   Tree's height = Person's height x Tree's shadow / Person's shadow

Substitution

   Tree's height = 6 x 38 / 8.5

Simplification

   Tree's height = 228 / 8.5

Result

    Tree's height = 26.8 ft  

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irakobra [83]

<h3><u>Answer:</u></h3>

  • B) 22.32 feet

\quad\rule{300pt}{1pt}

<h3><u>Solution</u><u>:</u></h3>

we are given that , a ladder is placed against a side of building , which forms a right angled triangle . We wre given one side of a right angled triangle ( hypotenuse ) as 23 feet and the angle of elevation as 76 ° . We can find the Perpendicular distance from the top of the ladder go to the ground by using the trigonometric identity:

\qquad\quad\bull ~{\boxed{\bf{ Sin\theta =\dfrac{Perpendicular}{Hypotenuse}}} }~\bull

Here,

  • hypotenuse = 23 feet
  • \theta = 76°
  • Value of Sin\theta = 0.97
  • Perpendicular = ?

\quad\dashrightarrow\quad \sf { sin\theta =\dfrac{P}{H}}

\quad\dashrightarrow\quad \sf { sin76° =\dfrac{P}{23}}

\quad\dashrightarrow\quad \sf { 0.97=\dfrac{P}{23}}

\quad\dashrightarrow\quad \sf {P = 0.97 \times 23 }

\quad\dashrightarrow\quad \sf { P = 22.32}

‎ㅤ‎ㅤ‎ㅤ~<u>H</u><u>e</u><u>n</u><u>c</u><u>e</u><u>,</u><u> </u><u>the </u><u>distance </u><u>from </u><u>the </u><u>top </u><u>of </u><u>the </u><u>ladder </u><u>to </u><u>the </u><u>ground </u><u>is </u><u>2</u><u>2</u><u>.</u><u>3</u><u>2</u><u> </u><u>feet </u><u>!</u>

\rule{300pt}{2pt}

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The graph is shown below

==================================================

Explanation:

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To solve for x, we undo the division. We'll multiply both sides by 6. That's how we get to x ≥ 42

The graph will involve a number line. Plot a closed filled in circle at 42 on the number line. Shade to the right. This visually represents any number that is 42 or larger. The endpoint 42 itself is included in the solution set.

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