Question

a) calculate the measure of $x$ in each.
where necessary, round you answer correct to one decimal place.
complete on a separate piece of paper.
1.
2.
3.
4.
5.
6.
7.
8.
9.

Explanation:

Step1: Apply Pythagorean theorem: $a^2+b^2=c^2$

1.

$x = \sqrt{9^2 + 12^2}$
$x = \sqrt{81 + 144} = \sqrt{225} = 15$

2.

$x = \sqrt{10^2 + 24^2}$
$x = \sqrt{100 + 576} = \sqrt{676} = 26$

3.

$x = \sqrt{7^2 + 3^2}$
$x = \sqrt{49 + 9} = \sqrt{58} \approx 7.6$

4.

$x = \sqrt{10^2 - 6^2}$
$x = \sqrt{100 - 36} = \sqrt{64} = 8$

5.

$x = \sqrt{24^2 - 6^2}$
$x = \sqrt{576 - 36} = \sqrt{540} \approx 23.2$

6.

$x = \sqrt{1^2 + 1^2}$
$x = \sqrt{1 + 1} = \sqrt{2} \approx 1.4$

7.

$x = \sqrt{21^2 - 8^2}$
$x = \sqrt{441 - 64} = \sqrt{377} \approx 19.4$

8.

$x = \sqrt{30^2 - 24^2}$
$x = \sqrt{900 - 576} = \sqrt{324} = 18$

9.

First find the hypotenuse of the large triangle: $L = 9+3=12$
For side $x$: $x = \sqrt{9^2 + 5^2} = \sqrt{81 + 25} = \sqrt{106} \approx 10.3$
For side $y$: $y = \sqrt{3^2 + 5^2} = \sqrt{9 + 25} = \sqrt{34} \approx 5.8$

Answer:

1. $15$
2. $26$
3. $\approx 7.6$
4. $8$
5. $\approx 23.2$
6. $\approx 1.4$
7. $\approx 19.4$
8. $18$
9. $x \approx 10.3$, $y \approx 5.8$