How to determine an exact expression for a horizontal distance?
Problem: Lynda is flying her kite at the end of a 40m string. The string makes an angle of Π/4 with the ground. The wind speed increases, and the kite flies higher until the string makes an angle of Π/3 with the ground. a) determine an exact expression for a horizontal distance that the kite moves between two positions. My solution so far: position 1 cos Π/4 = x /40 1/√2 = x /40 40/√2 = x position 2 cos Π/3 = x /40 1/2 = x /40 20 = x now i have to subtract these two expressions to get an answer of 20(√2-1) but i do not know how 40/√2 - 20 -thank you
Determine an exact expression for the vertical distance that the kite moves between the two positions. Trig Ratios for special angles.?
Draw diagram , use 2 right-angled triangles ---> vertial distance = 40sin(pi/3) - 40sin(pi/4) = 20(√ 3 - √ 2)
How do I make a diamond shape with asterisks in c++ using nested for loop?
Wanna print a diamond of stars???In C++???You're in for a treat!!!Here you go…#include
In an isosceles triangle, its two equal sides are 20 cm each and the angle between them is 45 degrees. What is the area of the triangle?
Consider any triangle [math]\Delta ABC.[/math]In right triangle [math]\Delta ABD,[/math][math]\sin \theta=\dfrac{BD}{AB}\tag*{}[/math][math]BD=AB\sin\theta\tag*{}[/math]The area of this triangle is easy right?[math]\operatorname{ar}{(\Delta ABC)}=\frac{1}{2}BD\cdot AC\tag*{}[/math][math]\operatorname{ar}{(\Delta ABC)}=\frac{1}{2}AB\cdot AC\sin\theta\tag*{}[/math]We can generalise this as follows, the area of a triangle with consecutive sides [math]a,b[/math] and included angle [math]\theta[/math] is [math]\frac{1}{2}ab\sin\theta.[/math]Apllying this to your question,[math]A=\frac{1}{2} 20\times 20\times\dfrac{1}{\sqrt{2}}\tag*{}[/math][math]A=100\sqrt{2}\text{ cm}^2\tag*{}[/math]
One angle of rhombus is given to be 60 degrees and its side is given 10 cm. Then, what will be the length of longer diagonal?
Suppose given rhombus is ABCD , with each side = 10 cm, smaller diagonal is BD & longer diagonal is AC , with point of intersection O.TO FIND: AC = ?< A = 60°=> triangle ABD is an equilateral triangle. as AB = AD hence base angles will be equal. & each will be of 60°Hence smaller diagonal BD = 10 cm => BO = 10/2 = 5 cmAs, diagonals of a rhombus, bisect each other at right angles.=> tri AOB is a right triangle with hypotenuse AB.AB² = BO² + AO²=> 10² = 5² + AO²=> AO = √(100 - 25)=> AO = √75 = 5√3 cm=> 2AO = 10√3 cm=> AC = 10√3 cm
Need Advice....Shattered Ankle?
In 2004 I fell and shattered my ankle..I have screws and plate in the both sides of my left ankle..things aren't going well with it as come to find out there are more problems with my foot..the doctor who did the surgery told me that there is nothing more that he can do so he sent me for a second opinion.. this doctor gave me pain patches to wear that did help some but I can feel my foot getting worse and it scares me..My daughter called me because she knows someone who did the same thing and his doctor told him that the plate and screws have to come out after a year because the bone does heal...they can't remove mine as I did alot of damage..they said the next step would to take out the nerve in my foot...would it be worth it to do or just learn to live with this pain..been having alot of spasms in my foot at night and it is really bothersome..I am also afraid of losing my foot but if I have to then it needs to be done...has anyone out there had this done??
Trigonometric ratios question?
to do this, you need the trig operation that relates hypotenuse (length of string) to adjacent (horizontal distance), with is cosine. a. u need to find the adjacent length when hypotenuse is 40 with an angle of pi/4, and the adjacent length when hypotenuse is 60 with angle of pi/3. x/40=cos(pi/4) x=1/rad(2) * 40 (since they want exact, you don't want to round this) but you can simplify it to 20rad(2) x/60=cos(pi/3) x=1/2*60=30 a)30-20rad(2) b) the kite moves horizontally further away since the second x is larger. c) to do this you need sine, and repeat whatever it is we just did. y/40=sin(pi/4) y=1/rad2*40=20rad2 y/60=sin(pi/3) y=rad3/2*60=30rad3 exact expression for vertical distance is 30rad3-20rad2. The altitude of kite above ground increases. (obviously, since the string got longer lol)