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3 years ago

How do you use special right triangles to solve for missing sides? (30-60-90 and 45-45-90 triangles)

Mathematics

1 answer:

Assoli18 [71]3 years ago

8 0

Answer: see below

Step-by-step explanation:

30 - 60 - 90 triangles have angles in the triangle measuring 30, 60, and 90 degrees. A 30 - 60 - 90 triangle also has special side ratios according to a side's location in the triangle.

The side across from the 30 degree angle is represented by x.

The side across from the 60 degree angle is represented by x $\sqrt{3}$ .

The side across from the 90 degree angle is represented by 2x.

45 - 45 - 90 triangles have angles in the triangle measuring 45, 45, and 90 degrees. A 45 - 45 - 90 triangle has special side ratios similar to the 30 - 60 - 90 triangle.

The side across from either of the 45 degree angles is represented by x.

The side across from the 90 degree angle is represented by x $\sqrt{2}$ .

These ratios can be used to find missing sides. If you know that a triangle is one of these special triangles and you also know one of its side lengths, you can plug the known length in for x in the proper place.

EX: you have a 30 - 60 - 90 triangle with a side length of 2 across from the 30 degree angle. You then know that the side across from 60 is 2 $\sqrt{3}$ and the side across from 90 is 4.

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A family plans a road trip from Fairbanks to Newbury. The distance between the two cities is 240 miles when traveling on the hig

alex41 [277]

Using proportions, it is found that the family will drive 482.8 km on the new route.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the family travels a distance of 125% of 240 miles, hence the distance is:

D = 1.25 x 240 = 300 miles.

Since there are are approximately <u>48.28 kilometers in 30 miles</u>, and 300/30 = 10, the distance in kilometers is given by:

D = 48.28 x 10 = 482.8 km.

More can be learned about proportions at brainly.com/question/24372153

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8 0

2 years ago

-2x-107-7x=3 I need help

inysia [295]

Start off by combining like terms, then get x by itself.
Lemme know if you still need help.

7 0

3 years ago

On a coordinate plane, square p q r s is shown. point p is at (4, 2), point q is at (8, 5), point r is at (5, 9), and point s is

Masteriza [31]

A statement which proves that the diagonals of square PQRS are perpendicular bisectors of each other is: option D.

<h3>How to calculate the slope of a line?</h3>

Mathematically, the slope of a line is given by the following formula;

$Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}$

For line RP, we have:

$Slope = \frac{9\;-\;2}{5\;-\;4}\\\\Slope = \frac{7}{1}$

Slope RP = 7.

For line SQ, we have:

$Slope = \frac{6\;-\;5}{1\;-\;8}\\\\Slope = \frac{1}{-7}$

Slope SQ = negative one-sevenths.

For the midpoint, we have:

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint on x-coordinate = (8 + 1)/2 = 9/2 = 4.5.

Midpoint on y-coordinate = (9 + 2)/2 = 11/2 = 5.5.

In conclusion, a statement which proves that the diagonals of square PQRS are perpendicular bisectors of each other is that the midpoint of both diagonals is (4.5, 5.5), the slope of RP is 7, and the slope of SQ is negative one-sevenths.

Read more on squares here: brainly.com/question/2882032

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