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A right triangle has a hypotenuse length of 13 units. One leg has a length of 12 units. Which equation can be used to determine

viktelen [127]

a = √(13² - 12²) units

<h3>Further explanation</h3>

<u>Given:</u>

A right triangle has a hypotenuse length of 13 units.
One leg has a length of 12 units

<u>Question:</u>

Which equation can be used to determine the length of the other leg?

<u>The Process:</u>

We will solve a problem regarding right triangles. In the process, there is a relationship between the Pythagorean Theorem with Exponent and Square Root.

Let us find out the equation to determine the length of the other leg. Let the length of the leg as "a".

The Phytagorean Theorem:

$\boxed{ \ (leg)^2 + (leg)^2 = (hypotenuse)^2 \ }$

$\boxed{ \ a^2 + 12^2 = 13^2 \ }$

Subtract by 12² on both sides.

$\boxed{ \ a^2 = 13^2 - 12^2 \ }$

To take the square root on both sides.

So here's the equation that can be used to determine the length of the other leg: $\boxed{\boxed{ \ a = \sqrt{13^2 - 12^2} \ }}$

- - - - - - - - - -

Notes

If we continue working on the above, the results will be as follows:

$\boxed{ \ a = \sqrt{13^2 - 12^2} \ }$

$\boxed{ \ a = \sqrt{169 - 144} \ }$

$\boxed{ \ a = \sqrt{25} \ }$

Hence the length of the other leg equal to a = 5 cm.

Of course, we agree with the use of the right intuition, which is to remember Pythagorean Triples, i.e., $\boxed{ \ 5-12-13 \ }.$ This method is very convenient when working on multiple-choice tests in a limited amount of time.

<h3>Learn more</h3>

What are the lengths of the legs of the triangle? brainly.com/question/13027296
Find out the measures of the two angles in a right triangle brainly.com/question/4302397
A word problem of a quadratic equation brainly.com/question/11805547

5 0

4 years ago

Write an equation in standard form of the line that passes through the given point and the given slope. (-9, -4); m = -1/3

tigry1 [53]

<h2>Answer:</h2>

First, we must determine <u><em>b</em></u> using <u><em>slope-intercept form*</em></u>, the given point, and the given slope.

$-4 = -\frac{1}{3}(-9) + b\\\\-4 = -3 + b\\\\-1 = b$

Second, we need to set up the equation of the line in slope-intercept form.

$y = -\frac{1}{3}x - 1$

Third, we convert the above equation to <em>STANDARD FORM**</em>.

$y = -\frac{1}{3}x - 1\\\\\frac{1}{3}x + y = -1$

We now have our equation: $\frac{1}{3}x - y = -1$

*Slope-intercept form: <em>y = mx + b</em>

**Standard form: <em>ax + by = c</em>

3 0

3 years ago

Why is it important to use triangles in tessellations

SpyIntel [72]

Because they are apart of the euclidean plane. <span />

8 0

3 years ago

It costs $25 for every 2-hour art class, how much would it cost for 6 hours of art classes

e-lub [12.9K]

Answer:

$75

Step-by-step explanation:

If it costs $25 for two hours and we want 6 hours, we simply multiply it by 3 because 6/2 = 3.

$25 * 3 = $75

7 0

3 years ago

Read 2 more answers

Simplify: (8t4 + 6 )+(914 – 2ť + 6t? – 6 )

vekshin1

Answer:t

2⋅(17t 2 −2t+6)

Step-by-step explanation:

v(8•(t4))+6)+((((9•(t4))-(2•(t3)))+(2•3t2))-6)

STEP

2

:

Equation at the end of step

2

:

((8•(t4))+6)+((((9•(t4))-2t3)+(2•3t2))-6)

STEP

3

:

Equation at the end of step

3

:

((8•(t4))+6)+(((32t4-2t3)+(2•3t2))-6)

STEP

4

:

Equation at the end of step

4

:

(23t4 + 6) + (9t4 - 2t3 + 6t2 - 6)

STEP

5

:

STEP

6

:

Pulling out like terms

6.1 Pull out like factors :

17t4 - 2t3 + 6t2 = t2 • (17t2 - 2t + 6)

(8•(t4))+6)+((((9•(t4))-(2•(t3)))+(2•3t2))-6)

STEP

2

:

Equation at the end of step

2

:

((8•(t4))+6)+((((9•(t4))-2t3)+(2•3t2))-6)

STEP

3

:

Equation at the end of step

3

:

((8•(t4))+6)+(((32t4-2t3)+(2•3t2))-6)

STEP

4

:

Equation at the end of step

4

:

(23t4 + 6) + (9t4 - 2t3 + 6t2 - 6)

STEP

5

:

STEP

6

:

Pulling out like terms

6.1 Pull out like factors :

17t4 - 2t3 + 6t2 = t2 • (17t2 - 2t + 6)

(8•(t4))+6)+((((9•(t4))-(2•(t3)))+(2•3t2))-6)

STEP

2

:

Equation at the end of step

2

:

((8•(t4))+6)+((((9•(t4))-2t3)+(2•3t2))-6)

STEP

3

:

Equation at the end of step

3

:

((8•(t4))+6)+(((32t4-2t3)+(2•3t2))-6)

STEP

4

:

Equation at the end of step

4

:

(23t4 + 6) + (9t4 - 2t3 + 6t2 - 6)

STEP

5

:

STEP

6

:

Pulling out like terms

6.1 Pull out like factors :

17t4 - 2t3 + 6t2 = t2 • (17t2 - 2t + 6)

5 0

3 years ago