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Chapter 3: Q. 2STP (page 150)

In the figure, $螖 MOQ$ is similar to $螖 NOP .$ What is the length of $\overset{炉}{MQ} ?$
(A) 12
(B) 12.5
(C) 19
(D) 21

Short Answer

Expert verified

The length of $\overset{炉}{M Q}$ is 21.

Step by step solution

01

Step 1. Sketch the given diagram

02

Step 2. Evaluate ∠NOP

Let $鈭� N O P = 胃 .$

$\begin{matrix} \sin 胃 = \frac{P e r p e n d i c u l a r}{H y p o t h e s i s} \\ = \frac{4.5}{9} \\ = \frac{1}{2} \\ 胃 = 30^{鈭�} \end{matrix}$

03

Step 3. Evaluate the length of MQ¯

Since $鈭� N O P = 30^{鈭�},$ $鈭� M O Q = 30^{鈭�} .$

$\begin{matrix} \sin 30^{鈭�} = \frac{P e r p e n d i c u l a r}{H y p o t h e s i s} \\ \frac{1}{2} = \frac{O Q}{M Q} \\ = \frac{O P + P Q}{M Q} \\ \frac{1}{2} = \frac{6 + 4.5}{M Q} \\ M Q = 2 脳 10.5 \\ = 21 \end{matrix}$

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