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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 right triangle, 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 Law of Sines 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 Law of Cosines 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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4 years ago

The following data gives the speeds (in mph), as measured by radar, of 10 cars traveling north on I-15. 76 72 80 68 76 74 71 78

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Answer:

71.123 mph ≤ μ ≤ 77.277 mph

Step-by-step explanation:

Taking into account that the speed of all cars traveling on this highway have a normal distribution and we can only know the mean and the standard deviation of the sample, the confidence interval for the mean is calculated as:

$m-t_{a/2,n-1}\frac{s}{\sqrt{n} }$ ≤ μ ≤ $m+t_{a/2,n-1}\frac{s}{\sqrt{n} }$

Where m is the mean of the sample, s is the standard deviation of the sample, n is the size of the sample, μ is the mean speed of all cars, and $t_{a/2,n-1}$ is the number for t-student distribution where a/2 is the amount of area in one tail and n-1 are the degrees of freedom.

the mean and the standard deviation of the sample are equal to 74.2 and 5.3083 respectively, the size of the sample is 10, the distribution t- student has 9 degrees of freedom and the value of a is 10%.

So, if we replace m by 74.2, s by 5.3083, n by 10 and $t_{0.05,9}$ by 1.8331, we get that the 90% confidence interval for the mean speed is: