The answer is 10
Because of the Pythagorean theorem, for sides of a right triangle (a triangle with one 90 degree angle) a, b, and c, where c is the hypotenuse (the side opposite the 90 degree angle), a^2 + b^2 = c^2.
We have a and b given in this problem, 6 and 8. We are solving for c. So 6^2 + 8^2 = c^2.
6^2 = 36, 8^2 = 64. 36 + 64 = 100. So c^2 = 100. The square root of 100 is 10, so c = 10.
Step-by-step explanation:
x= 2 y = 10
x= 0 y = 8
x= 4 y = 12
Answer: -4/5
Step-by-step explanation: It's important to understand
that perpendicular lines have negative reciprocal slopes.
"Negative reciprocal" is just a fancy way
of saying flip the fraction and change the sign.
So if we flip the fraction 5/4 we get 4/5 and
if we change the sign we get -4/5.
Answer:
x = 3√3
y = 6
Step-by-step explanation:
The geometric mean relations between segments intersecting the long hypotenuse and its parts can be used to find the values of interest.
<h3>Altitude</h3>
x = √(9·3) = 3√3
<h3>Short side</h3>
y = √((9+3)·3) = 6
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<em>Additional comment</em>
These right triangles are all similar, so corresponding sides are proportional. When the proportions are solved for a missing side, a geometric mean relation results. (The geometric mean of 'a' and 'b' is √(ab).)
Identify the segments above the horizontal line as w, x, y. (x and y are already identified in this figure.)
The ratio of short side to long side is ...
x/9 = 3/x ⇒ x² = 9·3 ⇒ x = √(9·3)
The ratio of short side to hypotenuse is ...
y/(9+3) = 3/y ⇒ y² = (9+3)·3 ⇒ y = √((9+3)·3)
Likewise, the ratio of long side to hypotenuse is ...
w/(9+3) = 9/w ⇒ w² = (9+3)·9 w = √((9+3)·9) = 6√3