It is known that the ratio of the hypotenuse of a right triangle to one right angle side is 17:8, and the length of the other right angle side is 60

17 × 17-8 × 8 = 9 × 25 = (3 × 5) × (3 × 5) = 15 × 15 ·· the other right angle side is 15 parts
60 ÷ 15 × 17 = 68 ··· oblique side length

Suppose that the two right angles of a right triangle are random numbers between < 0,1 > and try to find out the probability of the occurrence of events when the diagonal side length is less than 2 / 2

Let two right angles be x, y according to the meaning of the title: x ^ 2 + y ^ 2 < 1 / 2
The total region is 1, and the region that satisfies the condition that the diagonal side length is less than 2 / 2 is 1 / 4 * π * (root 2 / 2) ^ 2 = π / 8
So the probability is π / 8

If the lengths of the two right sides of a right triangle are random numbers in the interval (0, 1), then the length of the hypotenuse is less than 3 The probability of 4 is () A. 9π Sixty-four B. 9 Sixty-four C. 9π Sixteen D. 9 Sixteen

According to the meaning of the question, the question is a geometric model,
∵ two right angles are random numbers between 0 and 1,
Let two right angles be x, y
All events included in the test were {x, y| 0 < x < 1, 0 < y < 1}
The area of the corresponding square is 1,
The set {(x, y) | x2 + Y2 < 9 / 16, x > 0, Y > 0.}
This graph is a 1
Four circles, and the area is 9 π
64，
Then the length of the hypotenuse is less than 3
The probability of 4 is p = 9 π
64，
Therefore, a

Suppose that the lengths of the two right angles of a right triangle are random numbers in (0,1], then the probability that the length of the slanted side is less than 2 / 2 of the root is__ ?

It is equivalent to that every point in (0,1] * (0,1) of rectangular coordinate system is equal to possible, then the oblique side length < root 2 / 2 means that the distance from the point to the origin is less than the root 2 / 2, which is a 1 / 4 circle with the radius of root 2 / 2, and the area pi / 8, that is, the calculated probability

If the lengths of both right sides of a right triangle are any real numbers between 0 and 1, then event "oblique side length is less than 3 The probability of 4 "is______ .

Let two right angles be x, y respectively
Then we can get
0＜x＜1
0 ﹤ y ﹤ 1, the plane area is shown as square oabc, the area is 1
Note that "the length of inclined side is less than 3"
4 "is event a, then a:
0＜x＜1
0＜y＜1
x2+y2＜9
16 is 3
4 is the inner part of the radius circle and 1 in the square
The area of the circle is 1
4π×9
16＝9π
Sixty-four
From the calculation formula of geometric probability, P (a) = 9 π can be obtained
Sixty-four
So the answer is: 9 π
Sixty-four

In RT △ ABC, a and B are right angle sides and C are oblique sides. If a + B = 21 and C = 15, then the area of △ ABC is______ .

∵a+b=21，c=15，
(a + b) 2 = 441, that is, A2 + B2 + 2Ab = 441,
And ∵ A2 + B2 = C2 = 225,
∴2ab=216，∴1
2ab=54，
S △ ABC = 54
So the answer is: 54

Given that the sum of the two right angles of a right triangle is 10, how much is the length of the hypotenuse when the area is the largest?

Let one right angle side be x, the hypotenuse side be y, and the area is s, then the other right angle side is 10-x
S=X(10-X)/2
={25-(X^2-10X+25)}/2
=12.5-(X-5)^2/2
From this equation, we can see that when s = 12.5-0, s is the largest, that is, x = 5, that is, isosceles right triangle,
Y=√2*5^2=5√2

Given that the hypotenuse of a right triangle is 10 and the sum of the two right sides is 14, calculate the area of the right triangle

Let a right angle side be X
x²+(14-x)²=10²
x²+x²-28x+196=100
x²-14x+48=0
(x-6)(x-8)=0
x1=6,x2=8
When x = 6, 14-x = 8
When x = 8, 14-x = 6
The area of a right triangle is 6 × 8 △ 2 = 24

The length of the two right sides of a right triangle is 12, the length of the hypotenuse is 10, and the area is?

If the length of one right angle side is x, then the length of the other right angle side is 12-x

If the hypotenuse of a right triangle is 10 and the ratio of two right angles is 3 to 4, what is the area of the triangle

Let two right angles be 3x and 4x
Then the original formula is equal to (3x) 2 + (4x) 2 = (10) 2
The X of the solution is equal to 2
So the two right angles are 6 and 8
So area six times eight divided by two is 24

It is known that the ratio of the hypotenuse of a right triangle to one right angle side is 17:8, and the length of the other right angle side is 60