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Application of Pythagorean Theorem in Junior Middle School Mathematics
The first picture: solution: if the pole is x meters high, the rope length is x+ 1 meter.

x? +5? =(X+ 1)?

The solution is X= 12.

The second picture: ∫AC = 10 BC = 8 AC = 6.

∴AC? =BC? + AC?

That is, △ABC is a right angle △

∴ 1/2BP*AC= 1/2BC*AB

That is BP=4.8.

Let Xh enter the territorial sea first, according to Pythagorean theorem

( 12.8X)? +4.8? =8?

Solution X=0.5 hours.

The third picture: Solution: Assuming that Xs can reach the top of the mountain, according to Pythagorean theorem.

800? + 1500? =(50X)?

X = 170/5 = 34 minutes

Picture 4: As can be seen from the title:

(1) after half an hour, the first group of distances is s1= 30 * 30 = 900 m.

The distance of the second group S2=40*30= 1200m.

900? + 1200? =2250000= 1500?

According to Pythagorean theorem, the included angle is a right angle.

(2) Solution: Suppose that after X minutes, the two groups meet.

30X+40X= 1500

X= 150/7 minutes

Thanks for your hard work, I hope to adopt it ~ ~ ~