Hey guys! Just asking for some quick help.
In ABC , A is a right angle, and B = 45 degrees. What is the length of BC? If the answer is not an integer leave it in simplest radical form. The diagram has 11ft listed as height of the tall side
Answers:
11ft
11 sqrt 2
11 sqrt 3
22ft
It looks like BC is the hypotenuse.
method 1:
BC/11 = sin45
BC = 11sin45 = 11/(√2/2)
= 22/√2 * √2/√2
= 22√2 / 2 = 11√2
method 2:
BC^2 = 11^2 + 11^2
= 242
BC = √242 = 11√2
isosceles right triangle, 90 + 45 + 45 = 180
1^2 + 1^2 = 1+1 = 2
so ratios are 1, 1, sqrt 2
we want the hypotenuse
11 * sqrt 2
Avery
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What is the geometric mean of the pair of numbers? 96 and 6
The geometric mean of a pair of numbers is the square root of their product. So to find the geometric mean of 96 and 6, we can multiply them together and take the square root:
Geometric mean = √(96 × 6)
= √576
= 24
Therefore, the geometric mean of 96 and 6 is 24.
Thank you, Avery!
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What theorem or postulate proves the two triangles are similar? 6 12 3
AA Postulate
AS Postulate
SAS Theorem
SSS Theorem
In order to determine which theorem or postulate proves that two triangles are similar, we would need to know more information about the triangles.
The AA (Angle-Angle) Postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
The AS (Angle-Side) Postulate states that if an angle and the side adjacent to it in one triangle are congruent to an angle and the corresponding side in another triangle, then the triangles are similar.
The SAS (Side-Angle-Side) Theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are similar.
The SSS (Side-Side-Side) Theorem states that if the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar.
So, if we have more information about the sides and angles of the triangles, we could use one of these postulates or theorems to prove the similarity of the triangles.