Question

17)
6.5
9.9
19)
5.2
9.2
21)
5.3
7.2

Explanation:

Step1: Identify the problem type

These are right - triangle problems, and we can use the Pythagorean theorem $c^{2}=a^{2}+b^{2}$ (where $c$ is the hypotenuse and $a,b$ are the legs of the right triangle) to find the unknown side.

For problem 17:

We have a right triangle with one leg $a = 6.5$, hypotenuse $c=9.9$, and the other leg $x$ (let's call the unknown side $x$). From the Pythagorean theorem, $x^{2}=c^{2}-a^{2}$.
Substitute $c = 9.9$ and $a=6.5$ into the formula:
$x^{2}=9.9^{2}-6.5^{2}=98.01 - 42.25=55.76$
Then $x=\sqrt{55.76}\approx7.47$

For problem 19:

We have a right triangle with legs $a = 5.2$ and $b = 9.2$, and hypotenuse $c$. Using the Pythagorean theorem $c^{2}=a^{2}+b^{2}$.
$c^{2}=5.2^{2}+9.2^{2}=27.04 + 84.64=111.68$
$c=\sqrt{111.68}\approx10.57$

For problem 21:

We have a right triangle with one leg $a = 5.3$, hypotenuse $c = 7.2$, and the other leg $x$. Using the Pythagorean theorem $x^{2}=c^{2}-a^{2}$.
$x^{2}=7.2^{2}-5.3^{2}=51.84-28.09 = 23.75$
$x=\sqrt{23.75}\approx4.87$

Answer:

• Problem 17: The unknown side $\approx7.47$
• Problem 19: The hypotenuse $\approx10.57$
• Problem 21: The unknown side $\approx4.87$