How many axes of symmetry has a rhombus
1 answer:
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Answer:
Step-by-step explanation:
The first thing we are going to do is to fill in the other angles that we need to solve this problem. You could find ALL of them but all of them isn't necessary. So looking at the obtuse angle next to the 35 degree angle...we know that those are supplementary so 180 - 35 = the obtuse angle in the small triangle. 180 - 35 = 145. Within the smaller triangle we have now the 145 and the 10, and since, by the Triangle Angle-Sum Theorem all the angles have to add up to equal 180, then 180 - (10 + 145) = the 3rd angle, so the third angle is 180 - 155 = 25. Now let's get to the problem. If I were you, I'd draw that out like I did to keep track of these angles cuz I'm going to name them by their degree. In order to find d, we need to first find the distance between d and the right angle. We'll call that x. The reference angle is 35, the side opposite that angle is 12 and the side we are looking for, x, is adjacent to that angle. So we will use the tan ratio to find x:
Isolating x:
so
x = 17.1377 m
Now we have everything we need to find d. We will use 25 degrees as our reference angle, and the side opposite it is 12 and the side adjacent to it is
d + 17.1377, so that is the tan ratio as well:
and simplifying a bit:
and a bit more:
d + 17.1377 = 25.73408 so
d = 8.59, rounded
The completed table for the Pythagorean triples are:
.
A trio of positive numbers known as a Pythagorean triple fits into the Pythagoras theorem's formula, which is written as a² + b² = c², where a, b, and c are all positive integers. Here, "a" and "b" make up the other two legs of the right-angled triangle, and "c" serves as the triangle's "hypotenuse," or longest side. In terms of the Pythagorean triples (a, b, c).
In the question, we are given that a triangle with side lengths x² - 1, 2x, x² + 1 is a right triangle, and are asked to fill in the missing table:
.
Taking x as 3, and putting in the sides, we get:
x² + 1 = 3² + 1 = 10.
2x = 2*3 = 6.
x² - 1 = 3² - 1 = 8.
Thus, the triplet is 6,8,10.
For the triplet 8,15,17, we get the x value as:
2x = 8,
or, x = 8/2 = 4.
Thus, the x-value for the triplet (8,15,17) is 4.
Taking x as 5, and putting in the sides, we get:
x² + 1 = 5² + 1 = 26.
2x = 2*5 = 10.
x² - 1 = 5² - 1 = 24.
Thus, the triplet is 10,24,26.
For the triplet 12,35,37, we get the x value as:
2x = 12,
or, x = 12/2 = 6.
Thus, the x-value for the triplet (12,35,37) is 6.
Thus, the completed table for the Pythagorean triples are:
.
Learn more about the Pythagorean triplets at
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The provided question is incomplete. The complete question is:
"We know that a triangle with side lengths x² - 1,2x and x² + 1 is a right triangle. Using those side lengths, find the missing triples and x-values.
Write the triples in parentheses, without spaces between the numbers, and with a comma between numbers. Write the triples in order from least to greatest.
Type the correct answer in each box.
.