triangle

1. Optimising Area of a Triangle Given info 2 sides are equal et al - Calculating Maximu

Hi, I have a triangle with a perimeter of 3 (being each of the sides added). Two sides (lets say x) are the same length and I have to find the length of the third side (say z) that would optimise the area. Step 1: So: 2x + z = 3 z= 3-2x Now have z in term of x. Step 2...
2. Applied right triangle ( HELP )!!

Hi guys i know scanning a document and showing work is a frowned upon method but in this case its the only way i know how to do it, so in this problem i have linked the triangles by saying they all add up to 249 but i have too many variables. I don't know how to account for a in the x+z+c+a =...
3. Congruent Triangles Demonstration

Here is the following demonstration: In the figure PQ=QR, Angle 3 = Angle 4. Show that triangles PQS and PRT are congruent. I have tried several things here but none seem to work. I know that triangle PQR is isosceles. But that tells me that Angle P is equal to Angle R. From the figure it is...
4. Solve Triangle given value of Sin/Cos

In the diagram, AB = 33 and BC = 9. If \frac{\sin (0.5(\angle CAB - \angle CBA))}{\cos (0.5(\angle ACB))} = -0. \overline{57} , find AC. So far I've gotten that \sqrt{\frac{1 - \cos \angle CAB \cos \angle CBA - \sin \angle CAB \sin \angle CBA}{1 +\cos \angle ACB}} = \frac{-57}{99} using...
5. Determining cone to spherical triangle intersection

I have a sphere (x+x0)^2 + (y+y0)^2 + (z+z0)^2 = 1 formed of spherical triangles. The initial position of the sphere is not defined. Each triangle is determined by 3 normalized vectors (literally spherical triangle is part of a sphere bounded by three planes coming out of the sphere center)...
6. Finding the area of a triangle.

When finding an area of the triangle, you are given A=1/2bh, however, if there is no height it would be a=1/2absinthetta? Correct? And if you are given the height, where you use A=1/2bh, you can use any side for the base, ( besides the height)? Just wondering.
7. geometry triangle

The sides of triangle ABC are a, b and c. The sides of triangle MNP have the same measure of ABC medians. calculate the ratio of the areas ABC/MNP. Someone can help me?
8. Triangle finding h and the area of a gable.

Figure x is the length of a rafter measured from the top of a wall to the top of the roof; thetta is the acute angle between a rafter and the horizontal; and h is the vertical distance from the top of the wall to the roof. Suppose that thetta = 39.4 degrees, and x = 43.0 ft. (a) Determine h...
9. Right Triangle Problem (Answer Checking)

A building contractor wants to put a fence around the perimeter of a flat lot that has the shape of a right triangle. one angle of the triangle is 41.4 degrees, and the length of hypotenuse is 58.5m. Find the length of the fencing required. Round the answer to one decimal place. I got h =58.5...
10. Right Triangle Problem.

A ladder 18 ft long leans against a building. The ladder forms an angle of 60 degrees with the ground. (a) How high up the side of the building does the ladder reach? a= 15.59 ft (b)find the horizontal distance from the foot of the ladder to the base of the building b=9 ft I know how to get...
11. Triangle Sum 180 from Euclid's 5th axiom

I am working on a proof of the Triangle Sum Theorem by using Euclid's 5th axiom. Attached the picture so that you can see. So I started going in the other direction and saying well if \alpha+\gamma+\beta\prime \ge 180 then also \beta+\gamma+\alpha\prime \ge 180 and started working out that...

In ΔDEF, d = 7.5, <D = 50o, and <F = 60o. Solve the triangle.
13. Triangle and its Medial Triangle...

Can someone help with this? Theorem: A triangle and its medial triangle have the same centroid. The medial triangle of a triangle ABC is the triangle whose vertices are located at the midpoints of the sides AB, AC, and BC of triangle ABC. From an arbitrary point O that is not a vertex of...
14. Help calculating a point in 2d space on a rotating right angle triangle

I am trying to solve for a point on a triangle that rotates around a fixed point. For ease of calculation this point is at X: 0 Y: 0 The length and width of the triangle are always fixed, the only thing that changes is the rotation angle. How can I solve for X: ??? and Y: ??? taking into...
15. How to establish the position of sides in a triangle when finding the tangent

The answer given is 5/12. But how did they decide that instead of 13/12? Because the answer cannot be greater than one?
16. is this a 30 - 60 - 90 right triangle problem? need help solving

The answer given is square root of 10. But I thought that in a 30 - 60 - 90 right triangle that the hypotenuse is equal to twice the length of the shortest leg. Please help solve, thanks
17. Finding the third vertex of a triangle

The points A(0,3) and B(3,0) are the vertices of the base of the isosceles triangle ABC. What is the third vertex, if the medians AD and BE are perpendicular? I tried to solve this, but I got stuck after this. Thank you in advance.
18. Finding right triangle sides with only altitude

http://i.imgur.com/KuX5f8G.png Altitudes (AD; DE) is known, and all sides (AB; AC; BC) is known except EF and EG. I need formula to find them
19. Measuring the length of the sides of a triangle type problem?

I can't figure this out for the life of me(Crying). King Kong stands on the edge of the roof of a 62 foot high building. You poke your head out of a manhole and measure the angles of elevation to the top of King Kong's head and to his feet as 60 degrees and 59 degrees respectively.
20. Triangle Problem and help needed

The instructions indicate that x is solvable by using proportions. I don't see how this is possible. I'd appreciate any help. Thank you! Mark