Question #3063d

Question

Question #3063d

2 Answers

Impact of this question

1171 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-11T23:42:33

Check the method below.

Explanation:

Pythagorean's theorem states that in a right triangle, $a^{2} + b^{2} = c^{2}$ $a^2+b^2=c^2$ , where $c$ $c$ is your hypotenuse, or the angle opposite of the right angle, and $a$ $a$ and $b$ $b$ are either of your legs, or sides attached to the right angle.

For your first problem, you have both sides. Plug them into the theorem.

$3^{2} + 3^{2} = c^{2}$ $3^2+3^2=c^2$
$9 + 9 = c^{2}$ $9+9=c^2$
$18 = c^{2}$ $18=c^2$
$\sqrt{c^{2}} = \sqrt{18}$ $sqrt(c^2)=sqrt(18)$
$c = \sqrt{9} \sqrt{2}$ $c=sqrt(9)sqrt(2)$
$c = 3 \sqrt{2}$ $c=3sqrt(2)$

For your second problem, use the same theorem. However, note we're missing a leg and we have the hypotenuse already. Plug in accordingly.

$40^{2} + b^{2} = 65^{2}$ $40^2+b^2=65^2$
$1600 + b^{2} = 4225$ $1600+b^2=4225$
$b^{2} = 2625$ $b^2=2625$
$b \approx 51.2$ $b~~51.2$

Answer 2 · 2017-11-11T23:42:42

$a^{2} + b^{2} = c^{2}$ $a^2+b^2=c^2$

Explanation:

Each of these problems uses the Pythagorean Theorem/Pythagoras' Theorem.

This theorem states that for a right angled triangle with hypoteneuse $c$ $c$ and sides $a$ $a$ and $b$ $b$ , $a^{2} + b^{2} = c^{2} .$ $a^2+b^2=c^2.$ The hypoteneuse is the side opposite the right angle, and is always the longest side on a right angled triangle.
Google images

Example 1

For the first example, $a = 3$ $a=3$ and $b = 3$ $b=3$ .

$a^{2} + b^{2} = c^{2}$ $a^2+b^2=c^2$
$3^{2} + 3^{2} = c^{2}$ $3^2+3^2=c^2$
$c^{2} = 18$ $c^2=18$
At this point you can either take out your calculator to do $\sqrt{18}$ $sqrt18$ , or simplify the surd to get
$c = 3 \sqrt{2}$ $c=3sqrt2$

Example 2

For this problem, we need to re-arrange Pythagoras' theorem to make $a^{2}$ $a^2$ the subject (because its neater to have squares than square roots and squares).

$a^{2} + b^{2} = c^{2}$ $a^2+b^2=c^2$
$a^{2} = c^{2} - b^{2}$ $a^2=c^2-b^2$
Now, we sub in our values
$a^{2} = 65^{2} - 40^{2}$ $a^2=65^2-40^2$
$a^{2} = 4225 - 1600$ $a^2=4225-1600$
$a^{2} = 2625$ $a^2=2625$
Now using your calculator
$a = \sqrt{2625} = 5 \sqrt{105} \approx 51.2 f t$ $a=sqrt2625=5sqrt105~~51.2ft$

Science

Math

Humanities

... and beyond

Question #3063d

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question