The diagrams are shown below.
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Problem 1
We have a right triangle with horizontal leg [tex]a = 7[/tex] and hypotenuse [tex]c = 25[/tex] to represent the length of the ladder. Use the pythagorean theorem to find the vertical leg b.
[tex]a^2+b^2 = c^2\\\\7^2+b^2 = 25^2\\\\49+b^2 = 625\\\\b^2 = 625-49\\\\b^2 = 576\\\\b = \sqrt{576}\\\\b = 24[/tex]
Answer: 24 feet
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Problem 2
After 1 hour, the first jet has traveled 300 miles while the other has traveled 400 miles. Use the formula
[tex]\text{distance = rate*time}[/tex]
We'll have a right triangle with the two legs of [tex]a = 300 \text{ and } b = 400[/tex]. The order of 'a' and b doesn't matter.
Use the pythagorean theorem to find the hypotenuse c.
[tex]a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{300^2+400^2}\\\\c = \sqrt{90,000 + 160,000}\\\\c = \sqrt{250,000}\\\\c = 500\\\\[/tex]
The two jets are 500 miles apart after one hour.
Answer: 500 miles
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Problem 3
We have a right triangle with horizontal leg 80 meters and vertical leg 30 meters. The hypotenuse is the distance you travel.
[tex]a^2+b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{30^2+80^2}\\\\c = \sqrt{900+6400}\\\\c = \sqrt{7300}\\\\c = \sqrt{100*73}\\\\c = \sqrt{100}*\sqrt{73}\\\\c = 10\sqrt{73}\\\\c \approx 85.440037[/tex]
Exact Answer: [tex]\boldsymbol{10\sqrt{73}}[/tex] meters
Approximate answer: 85.440037 meters
