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In the right triangle ABC, the angle c = 90 degrees, the angle cab = 30 degrees, ab = 2, take a as the origin, the line AB is the positive half axis of the X axis, establish the rectangular coordinate system, let e (T, 0), f (T + 1,0) slide on the line AB, note that the area of the triangle ABC between the straight lines X = t and x = t + 1 is y, and Y is expressed as a function of T by analytic formula
This is a piecewise function. Through point C, we make CD ⊥ AB, the foot of the foot is D, mark the intersection letter of the line x = t and AC as G, and mark the intersection point of the line x = t + 1 with AC as h, then because AB = 2, cab = 30, CA = √ 3, CB = 1. According to the equal area method, ab × CD = CB × Ca, CD = √ 3 / 2, ad = 3 / 2
In the right triangle ABC, the angle a = 30 degrees, B = 60 degrees, C = 90 degrees, AC = 6?
AB=6÷√3×2=4√3
In a right triangle, where ∠ C = 90 ° a.bc is the opposite side of the angle a ∠ B ∠ C. If a = 15, B = 20, then the circumference of △ ABC is If a = 2C = 2.5, then what is the area of △ ABC? If a; C = 3; 5A + C = 32, then B = how much; if C = 10A; b = 3; 4, then a = how much; b = how much is the height on the bevel edge equal to
According to Pythagorean theorem, the hypotenuse C is equal to 25
In the right triangle ABC, the angle c = 90 degrees, AC = 6 cm, BC = 8 cm. Starting from point a, the moving point P moves to point C at the speed of 1 cm / s on the line AC At the same time, Dongdian Q starts from point B and moves to point a at the speed of 2 cm / s on the line ba. When a moving point moves to the end point first, the whole movement process ends. Let P and Q move for T seconds. (1) let the area of triangle Apq be y, please find y and (1) let the area of triangle Apq be y, and then find the functional relationship between Y and t, Write out the range of t to be straight. Find out the area of triangle Apq when t is straight. (2) in the whole process of motion, whether there is a triangle with points a, P, Q as the vertex similar to triangle ABC? If there is, find t; if not, explain the reason
(1) 1. Right triangle ABC middle angle c = 90 degrees AC = 6cm BC = 8cm
So AB = 10
AP=1*T=T,BQ=2*T=2T
AQ=10-2T
Make QD vertical AP
Using similarity: QD: 8 = QA: 10, QD can be obtained
The area of triangle Apq y = AP * QD / 2 = 8t-8t ^ 2 / 5 (0 〈 = 5)
2. The maximum area of triangle Apq is y = - 8t ^ 2 / 5 + 8t
=-8/5（T-5/2）^2+10
When t = 5 / 2, the area of triangle Apq is the largest
(2) Two cases
1. When QP / / BC, AP: 6 = AQ: 10
T：6=（10-2T）：10,T=30/11
2. When QP is perpendicular to AB, AP: 10 = AQ: 6
T：10=（10-2T）：6 T=50/13
As shown in the figure, in the right triangle ABC, the angle c = 90 °, the angle a = 30 °, BD is the bisector of angle ABC, ad = 20, find the length of BC
Make de perpendicular to E
Because the angle AED = 90 °, angle a = 30 °, ad = 20
So de = 1 / 2ad = 10
Because BD is the bisector of angle ABC, De is vertical AB, DC is vertical BC
So DC = de = 10
So AC = AD + DC = 20 + 10 = 30
Because the angle c = 90 ° and the angle a = 30 °
From Pythagorean theorem, BC = 10 times root 3
In a right triangle, the angle c is equal to 90 ° and AC: BC = 3:4, ab = 20. Find the s triangle ABC
According to Pythagorean theorem
5x=20 x=4
AC=12,BC=16
S=12*16/2=96
As shown in the figure, in RT triangle ABC, ∠ B = 90 °, BC = 5, root sign 3, ∠ C = 30 °, point d starts from point C and moves along CA direction at a speed of 2 per second. At the same time, point e starts from point a and moves uniformly to point B at the speed of 1 per second in AB direction. When one of them reaches the end point, the other point also stops moving. The time for point D.E to move is T seconds, and point D is used as DF ⊥ BC to connect de and ef (1) It was proved that AE = DF (2) Can a quadrilateral aefd become a diamond? If so, find out the corresponding value of T; if not, please explain the reason (3) When t is what value, triangle def feeds RT triangle? Please explain the reason
From the Pythagorean theorem of right triangle, we can get AB = 5, AC = 10
CD=2t AE=t
(1)DF:AB=CD:AC DF:5=2t:10 DF=t=AE
(2) If it can, then ad = 10-2t = t = AE, t = 10 / 3
At this time, CD: AC = 2T: 10 = 2:3 = CF: CB BF: BC = 1:3 be: Ba = 1-ae: ab = 1-2 / 3 = 1 / 3
So EF / / AC
So it's diamond shaped, and at this point
Respondent: teacher024
(3)
CF:CB=CD:CA=t:5
If the triangle DEF is a right triangle and can only be ∠ EDF = 90 °, then the quadrilateral BEDF is a rectangle
DE=BF,DF=BE
Because DF = AE
So e is the midpoint of AB, so t = 5 / 2 / 1 = 2.5
Given the right triangle ABC, angle c = 90 degrees, angle a = 60 degrees, a + B = 3 + (3 root sign 3), then a=_____
Angle c = 90 degrees, angle a = 60 degrees, so angle B = 30 degrees
TGA = A / b = (root 3), so a = (b * root 3) is because a + B = (3 + 3 root sign 3)
B = 3, a = 3, root sign 3
Given that the angle c of right triangle ABC is 90 degrees, a + B + C = 2 + radical 6, the center line of AB side is 1, find a B C
The center line on the hypotenuse is half the length of the hypotenuse
So the length of the hypotenuse is 2
A + B = radical 6
According to Pythagorean theorem
a²+b²=c²=4
ab=[(a+b)²-a²-b²]/2=1
Therefore, a and B are two of the quadratic equations of one variable with root 6x + 1 = 0
X = (Radix 6-radix 2) / 2 or x = (Radix 6 + Radix 2) / 2 are obtained
A = (Radix 6-radix 2) / 2, B = (Radix 6 + Radix 2) / 2, C = 2
or
A = (Radix 6 + Radix 2) / 2, B = (Radix 6-radix 2) / 2, C = 2
In △ ABC, the three sides of AB, BC and AC satisfy AB: BC: AC = 1:3: root 10. Try to judge whether △ ABC is a right triangle
∵ AB: BC: AC = 1:3: root 10
If AB = k, then BC = 3k, AC = √ 10K
∵AB²+BC²=10k²=(√10k)²=AC²
Ψ B = 90 ° is a right triangle
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