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3 years ago

How do you find the length of a leg on a triangle?

Mathematics

2 answers:

shutvik [7]3 years ago

7 0

9514 1404 393

Answer:

law of sines
law of cosines
Pythagorean theorem
area formula

Step-by-step explanation:

The method for finding the unknown length of a side of a triangle depends on what other information is given. In general, you need one side, one angle, and at least one other side or angle.

Solving a triangle usually is introduced with the Pythagorean theorem. For a <em>right triangle</em>, it tells you ...

the square of the hypotenuse is equal to the sum of the squares of the other two sides.

If the side lengths are a, b and the hypotenuse is c, then ...

c² = a² + b²

Solving for the hypotenuse, c, you have ...

c = √(a² +b²)

Solving for one side, a, you have ...

a = √(c² -b²)

Occasionally, you're asked to find a measure of a triangle using the formula for area.

A = 1/2bh

Solving for the base or height gives you ...

b = 2A/h

h = 2A/b

Once you learn trigonometry, additional methods are available for solving triangles. The <em>Law of Sines</em> tells you ...

a/sin(A) = b/sin(B) = c/sin(C)

where angles A, B, C are opposite sides a, b, c, respectively.

And the <em>Law of Cosines</em> tells you ...

c² = a² +b² -2ab·cos(C) . . . . . . . . where sides and angles are as above

This can be rearranged by interchanging a, b, c, keeping the appropriate angle. For C = 90°, this reduces to the Pythagorean theorem.

For right triangles, the various trig relations can also be used to solve triangles. These are conveniently summarized in the mnemonic SOH CAH TOA. It is intended to remind you ...

Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent

In summary, depending on the given information, you choose an applicable formula, fill in the given information, and solve for the unknown. If you have more than one unknown, you may need to choose a different formula.

Darya [45]3 years ago

4 0

Answer:

add the other lenghts togethere and subtrack those 2 from 180 and bam

Step-by-step explanation:

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What is the range of the function graphed below?

Fynjy0 [20]

Answer:

-3<y<=3 or B

Step-by-step explanation:

first we find the smallest y value which is -3

then we find the largest y vlaue which is three

so since there is an open circle at negative three we do not include it while at three we do.

so the answer would be -3<x<=3

if my answer helps please mark as brainliest.

8 0

3 years ago

I need help with #61 to #64 ASAP please and thank you …. Could someone please help me with it… I need to get it done ASAP

aivan3 [116]

Problem 61

The nth triangular number is

T(n) = n(n+1)/2

I'll rewrite this into

T(n) = 0.5n(n+1)

The triangular number right after this is

T(n+1) = 0.5(n+1)(n+2)

I replaced every n with n+1 and simplified

Let's see what we get when we add up the two expressions

T(n) + T(n+1)

0.5n(n+1) + 0.5(n+1)(n+2)

0.5n^2+0.5n + 0.5(n^2+3n+2)

0.5n^2 + 0.5n + 0.5n^2 + 1.5n + 1

n^2+2n+1

(n+1)^2

This shows that the sum of any two consecutive triangular numbers results in a square number

Here's a few examples

0+1 = 1
1+3 = 4
3+6 = 9
6+10 = 16
10+15 = 25

Note each sum is a perfect square, which visually would plot out a square figure.

For quick reference, the set of the first few triangular numbers is {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55,...}

<h3>Answer: Square number</h3>

==========================================================

Problem 64

Let's say we go with n = 5.

This means,

T(n) = 0.5n(n+1)

T(n-1) = 0.5(n-1)(n-1+1)

T(n-1) = 0.5n(n-1)

T(5-1) = 0.5*5(5-1)

T(4) = 10

This says that when n = 5, the 4th triangular number is 10

Triple that result and add on n = 5

3*T(4) + n = 3*10+5 = 35

This result is beyond obvious which category of figurate number it belongs to. It's not a triangular number since it's not in the form n(n+1)/2. It's not a square number either.

Through a bit of trial and error, you should find it's a pentagonal number

Pentagonal numbers are of the form n(3n-1)/2

If you plugged n = 5 into that, it leads to 35

n(3n-1)/2 = 5*(3*5-1)/2 = 5*14/2 = 70/2 = 35

The diagram shown below represents the first few pentagonal numbers. The number of blue dots corresponds to the pentagonal number itself. Note the equal spacing when dealing with dots on each segment (eg: some interior blue dots are midpoints, others are quarter points, etc.)

<h3>Answer: Pentagonal number</h3>