Question

PLS HELP ( CORRECT GETS BRAINLY )



ED = 5.49 miles. Find EH.

Answer 1

$\bullet\: \: {\large{ \underline{ \underline{ \frak{ \purple{Given :: }}}}}}$

$\quad \cdot\dashrightarrow \: \: \bf{ED = {\textit { \textbf{5.49}}} \: mi}$

$\quad \cdot\dashrightarrow \: \: \bf{CD = {\textit { \textbf{4000}}} \: mi}$

$\quad \cdot\dashrightarrow \: \: \bf{CH = {\textit { \textbf{4000}}} \: mi}$

$\bullet\: \: {\large{ \underline{ \underline{ \frak{ \blue{To \: Find :: }}}}}}$

$\quad \cdot\dashrightarrow \: \: \bf{EH}$

$\bullet\: \: {\large{ \underline{ \underline{ \frak{ \pink{Theorem \: Used :: }}}}}}$

$\quad \cdot\dashrightarrow \: \: \bf{Pythagoras \: theorem}$

$\bullet\: \: {\large{ \underline{ \underline{ \frak{ \red{Explanation :: }}}}}}$

$\qquad \quad\: \: \: \bf {\underbrace{ \underline{Finding \: EC : }}}$

➦ Here, we can see in the attached diagram that :

$\quad \cdot\dashrightarrow \: \: \bf{EC = CD + ED}$

$\quad \cdot\dashrightarrow \: \: \sf{EC = {\textit { \textbf{4000 + 5.49}}}}$

$\quad \cdot\dashrightarrow \: \: \underline{\boxed{\bf{EC = {\textit { \textbf{4005.49}}}}}}$

$\qquad \quad\: \: \: \bf {\underbrace{ \underline{Finding \: EH : }}}$

➦ Here, by using Pythagoras theorem to find EH, we get :

$\quad \cdot\dashrightarrow \: \: \bf{EC^2 = EH^2 + CH^2}$

➦ By Substituting the known values, we get :

${\quad \cdot\dashrightarrow \: \: \bf{\textit { \textbf{4005.49}}}\:^2 = EH^2 + {\textit { \textbf{4000}}}\:^2}$

➦ Then, we have to subtract 4000² from 4005.49² :

${\quad \cdot\dashrightarrow \: \: \bf{\textit { \textbf{4005.49}}}\:^2 - {\textit { \textbf{4000}}}\:^2 = EH^2 }$

${\quad \cdot\dashrightarrow \: \: \bf{\textit { \textbf{4005.49}}}\:^2 - {\textit { \textbf{4000}}}\:^2 = EH^2 }$

${\quad \cdot\dashrightarrow \: \: \bf{\textit { \textbf{43,950.14}}}\approx EH^2 }$

➦ Then, by taking square root, we get :

$\quad \cdot\dashrightarrow \: \: \underline{\boxed{\bf{\textit { \textbf{210}}}\approx EH}}$

.°. EH ≈ 210 mi.

Answer 2

Answer :

ㅤㅤ→ EH ≈ 210 mi.

Step-by-step Explanation :

Given that :

ㅤㅤ→ ED = 5.49 mi.

ㅤㅤ→ CH = 4000 mi.

ㅤㅤ→ CD = 4000 mi.

To find :

ㅤㅤ→ Measurement of = EH .

Finding the measurement of EH :

Measurement of EC :

ㅤㅤ→ EC = CD + ED .

ㅤㅤ→ EC = 4000 + 5.49 .

ㅤㅤ→ EC = 4005.49 mi.

By Pythagoras' theorem :

ㅤㅤ→ EC² = EH² + CH².

Measurement of EH :

ㅤㅤ→ 4005.49² = EH² + 4000².

ㅤㅤ→ 4005.49² - 4000² = EH².

ㅤㅤ→ 43950.14 ≈ EH².

ㅤㅤ→ √43950.14 ≈ EH.

ㅤㅤ→ 210 ≈ EH.

ㅤㅤ→ EH ≈ 210.

.°. The measurement of EH is approximately 210 mi.