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Chapter 10: Problem 1

In questions 1-11 \(\Delta \mathrm{ABC}\) has a right angle at \(\mathrm{C}\). Calculate \(\mathrm{AB}\) given \(\mathrm{AC}=9 \mathrm{~cm}\) and \(\mathrm{BC}=15 \mathrm{~cm}\)

Short Answer

Expert verified
Answer: The length of the hypotenuse AB is approximately 17.49 cm.

Step by step solution

01

Recall the Pythagorean theorem

The Pythagorean theorem states that for a right triangle with legs of length a and b, and a hypotenuse of length c: \(a^2+b^2=c^2\). We will use this theorem to find the length of the hypotenuse AB.
02

Identify the given lengths

We are given that AC = 9 cm and BC = 15 cm. We can assign AC = a and BC = b, so we have a = 9 and b = 15.
03

Apply the Pythagorean theorem

Using the Pythagorean theorem, we will plug in the values of a and b into the formula and solve for c: \(a^2+b^2=c^2\) \((9)^2+(15)^2=c^2\)
04

Calculate the squares of a and b

Now, we will calculate the squares of a and b and then add the two values together: \((9)^2 = 81\) \((15)^2 = 225\) \(81 + 225 = 306\) So, the equation becomes: \(306 = c^2\)
05

Find the length of the hypotenuse

To find the length of the hypotenuse (c), we will take the square root of both sides of the equation: \(\sqrt{306} = c\) Approximating the square root of 306, we get: \(c \approx 17.49\) So, the length of the hypotenuse AB is approximately 17.49 cm.

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Most popular questions from this chapter

In questions 1-11 \(\Delta \mathrm{ABC}\) has a right angle at \(\mathrm{C}\). Calculate \(\mathrm{AC}\) given \(\mathrm{BC}=12 \mathrm{~cm}\) and \(B=53^{\circ}\)

For questions \(1-10\) solve \(\triangle \mathrm{ABC}\) given \(\mathrm{BC}=14 \mathrm{~cm}, \mathrm{AB}=20 \mathrm{~cm}, C=50^{\circ}\)

In questions \(1-10\) solve \(\triangle \mathrm{ABC}\) given \(\mathrm{AC}=105 \mathrm{~cm}, \mathrm{AB}=76 \mathrm{~cm}, A=29^{\circ}\)

In questions 1-11 \(\Delta \mathrm{ABC}\) has a right angle at \(\mathrm{C}\). Calculate BC given \(\mathrm{AB}=27 \mathrm{~cm}\) and \(B=32^{\circ}\).

For questions \(1-10\) solve \(\triangle \mathrm{ABC}\) given \(A=37^{\circ}, B=47^{\circ}, \mathrm{AB}=17 \mathrm{~cm}\)
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