Question

fill in the missing angles and then state if the triangles in each pair are similar. if so, state how you know they are similar and complete the similarity statement.
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1. mr. sullivan is lost at sea and freaking out in his little sailboat. he will swim for the shore if he is 70 meters or less. find ( x ) and decide if sully should swim for it (his life depends on it).

Explanation:

Step1: Use the property of similar triangles

Since the two right - angled triangles are similar (by AA similarity, as they both have a right angle and share an angle), we can set up the proportion \(\frac{x}{20}=\frac{100 + 25}{25}\).

Step2: Solve the proportion for \(x\)

Cross - multiply: \(25x=20\times(100 + 25)\).
First, calculate \(20\times(100 + 25)=20\times125 = 2500\).
Then, \(x=\frac{2500}{25}=100\).

Answer:

\(x = 100\) meters. Since \(100>70\), Mr. Sullivan should not swim for the shore.