That diagram is ok, but my answer "Area of a triangle QRP = 3√3" is NOT correct!!!
The correct answer is [QRP] = 5.569219381 square units!!!
(I don't know how to convert that decimal into radical.)
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or space by the same distance in a given direction.
A rotation is a transformation that turns a figure about a fixed point called the center of rotation.
• An object and its rotation are the same shape and size, but the figures may be turned in different directions.
• Rotations may be clockwise or counterclockwise.
In the coordinate plane, A = (0,0), B = (0,4), and C = (5,0). If P is a point inside triangle ABC such that AP = sqrt(10) and BP = 3*sqrt(2), then find CP.
Use the law of cosines to find ∠BAP. Find ∠PAC
Using ∠PAC and line AP, calculate line segments AD and PD
CP = sqrt[PD2 + (AC - √8)2] ==> CP ≈ 2.591
Question: If the area of triangle ABC is 27, what is the value of p?
In my above post, I was using the wrong diagram.
Answer: A (3, 12) B (12, 0) C (0, p)
1/ AB = arctan(12 / 9) = 15
2/ CY = 2*27 / 15 = 3.6
3/ ∠ABO ≅ ∠YCZ = arctan(12 / 9) = 53.13010235º
4/ OZ = 12 * tan ∠ABO = 16
5/ CZ = CY / cos∠YCZ = 6
6/ p = OZ - CZ = 10
( See above diagram )
If the area of triangle ABC is 27, what is the value of p?
Solving this geometry problem in several easy steps:
1) AB = sqrt(122 + 102) = 15.62049935
2) CY = 2*27 / AB = 3.456995759
3) ∠ABO ≅ ∠ YCZ = arctan(12 / 10) = 50.19442891º
4) OZ = 12 * tan∠ABO = 14.4
5) CZ = CY / cos∠YCZ = 5.4
6) p = OZ - CZ = 9
Sides of an obtuse triangle AB, BC, and AC have midpoints E, F, and D. G is the point of intersection of all 3 medians.
If AB = 7, BC = 9, and BG = 3 then what's the length of AC? (AC is the longest side)
The Median Theorem states that the medians of a triangle intersect at a point called the centroid that is two-thirds of the distance from the vertices to the midpoint of the opposite sides.
If BG is 3 then BD = 3 * 1.5 = 4.5
Since we have: AB=7, BC=9, and BD=4.5 we can use Apollonius's theorem to find AC.
|AB|2 + |BC|2 = 2( |AD|2 + |BD|2 )
AC = 2|AD| ≈ 13.379
A right triangle has legs of length 6 and b and a hypotenuse of length c.The perimeter of the triangle is18.Compute c.
a = 6 b = 6 / tanA c = sqrt[62 +(6 / tanA)2]
We'll use this information to calculate the angle A a + b + c = 18
6 + 6 / tanA + sqrt[62 + (6 / tanA)2] = 18 angle A = 53.13010235º
Side b = 6 / tanA = 4.5
Side c = sqrt(a2 + b2) = 7.5