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Help on these problems:
1)In triangle GHI, we have GH = HI = 25 and GI = 40. What is sin <GIH?
2)In triangle GHI, we have GH = HI = 25 and GI = 30. What is sin <GHI?
3)In triangle PQR, we have angle P = 90 degrees, QR = 15, and tan R = 5 cos Q. What is PQ?
this is what I did so far:
Let the coordinates of the points in triangle ABC be A(0,0), B(a,0), and C(c,d). Since D is the midpoint of BC, the coordinate points of D are
I was planning to make equations for lines AC and DE and find the intersection which would be the coordinates for point E. I made an equation for line AC which is y=d/c x. However, when I tried to create an equation for line DE, the y-intercept seemed very complicated: y=-c/d x+(ac+c^2+d^2)/2d. I tried solving for x and y, but the fractions didn't come out as easy numbers to work with.
Can someone see if I made an error?
Triangle ABC has vertices A(0, 0), B(0, 3) and C(5, 0). A point P inside the triangle is sqrt{10} units from point A and sqrt{13} units from point B. How many units is P from point C? Express your answer in simplest radical form.
How do we know that AH=AJ and EF=DM/AM?
I see it now
I also need help on this problem:
A water-filled spherical balloon lands on a sidewalk, momentarily flattening to a hemisphere. The ratio of the radius of the spherical balloon to the radius of the hemisphere can be expressed in the form sqrt[3]{a} for some real number a. Compute a.
Thanks so much!
I've been bashing my brain to solve this problem for days, but I don't know how to solve it. It seems really easy though. Please help:
The volume of a cylinder is 60 cubic centimeters. What is the number of cubic centimeters in the volume of the sphere it circumscribes?
How do we know triangles SAQ and SDR are similar? (I hope I have my diagram correct) So, is SR a straight line and if it is, how do we know that? To be clear, point S is created when we extend CP and AD right??? Thank you in advance!
i) Prove the triangles are similar using AA similarity.
ii) We don't need to prove that RS is straight. We can just say that we extended QR and DA and the point of intersection is S.
iii) Yes, point S is created when we extend CP and AD.
I see how you've got your answer but the answer still isn't correct. I don't understand why though.
Here's the exact wording of the problem:
We are given a cube of side length 2. We then slice a pyramid off each corner, as shown, so that every side length of the remaining polyhedron has the same length. Let A, P, Q, and R be the vertices shown. Let x = AP, y = AQ, and z = AR. Convince yourself that x=y=z. Don't forget here that all we know is that the edges of all of the octagons are the same length. Find x.
Thank you so much bob!
I've tried how you told us to do the problem, but I got the answer wrong too.
Here's the link:
http://latex.artofproblemsolving.com/b/ … 1f27d7.png
Could we do this without a 3D coordinate plane?
I got a hint to solve this problem:
Let the plane through C, P, and Q intersect \overline{AD} at S. What can you say about the diagram? Which two-dimensional figures can you work with?
Thanks so much!
How about the second question?
Also, can I have help on this problem too:
Let ABCD be a regular tetrahedron and let P be the unique point equidistant from points A,B,C,D. Extend AP to hit face BCD at point Q. What is the ratio PQ/AQ?
Let ABCD be a regular tetrahedron. (A regular tetrahedron is a pyramid in which all four faces are equilateral triangles.) The centers of the faces of tetrahedron ABCD are connected to form another regular tetrahedron EFGH. Let V1 and V2 be the volumes of tetrahedra ABCD and EFGH, respectively. Find V1/V2.
I know the volume of a regular tetrahedron is s^3/6sqrt(2) where s is the edge length. But I don't know how to find the edge length of EFGH.
I see it now, thank you so much bob!
I still don't understand the property of the circle that makes angle BAP=ADP.
Is there another way to show that the triangles are similar?
I've tried using angle chasing, but I don't know which angles I should use to represent with the variables x and y.
I got it. Thank you so much for the help!
A right cylindrical oil tank is 15 feet tall and its circular bases have diameters of 4 feet each. When the tank is lying flat on its side (not on one of the circular ends), the oil inside is 3 feet deep. How deep, in feet, would the oil have been if the tank had been standing upright on one of its bases? Express your answer as a decimal to the nearest tenth.
Could you help me solve this problem? Thanks!
But how do I compute the angles of triangle DEF in terms of the angles of triangle ABC? I've found 3 isosceles triangles so far, but I don't know what to do with them.
Can you provide me some hints for this proof?
Let the incircle of triangle ABC be tangent to sides BC, AC, and AB at D, E, and F, respectively. Prove that triangle DEF is acute.
http://latex.artofproblemsolving.com/5/e/9/5e95ff0f346c35f3a6cc9ae53d6ce2dc585bb21e.png
I know I have to use inscribed angles. Any other helpful hints?
Thanks!
I'm using the pythagorean theorem and thale's
Thanks for the help!!!
i got 197, but it's not correct. I don't know what i did wrong
Help on this question:
The second hand on the clock pictured below is 6 cm long. How far in centimeters does the tip of this second hand travel during a period of 30 minutes? Express your answer in terms of pi.
