Trigonometry

You want to clean some leaves out of a gutter on your roof. The gutter is 8m above the ground. You want the top of the ladder to rest against the wall no more than 50cm below the gutter. You don't want the ladder to make an angle any steeper than 80 degrees from the horizontal. What is the shortest ladder you coud use?

Opposite / adjacent

It is 2.

It is approx 0.2679

the simple way to culculate this value is to ist consider the basic trignometric ratio near to 20. Than we come that 30 is near to it and cos30 is equal to 0.866 now for 1 dgree rise or fall the costheta decrese by the factor 0.0009 since cos20 is 10 dgree far frm thrty so multiply 0.0009 by 10 and subtract from 0.866. U wil get answer of cos20

for what number of tereahedra exist kaleidocycle

The ones you cant see.

Sides have lenght, angles do not.

Cosine is the ratio of the adjacent side to the hypotenuse. Cosine can be used to find either of these sides if the other is known.

Meaningless question

You cannot. With only the base given (a parallelogram) you don't even know what the shape is: it could be a parallelepiped, or a parallelogram based pyramid or one of several other shapes.

Divide the height of the ramp by the length of the ramp (rise over run).

3*pi/4, 7*pi/4, 11*pi/4 and 15*pi/4 radians or2.3562, 5.4978, 8.6394 and 11.7810 radian (approx).

No, trigonometry can be used with any triangle, right angle or not.

While the primary trigonometric functions are defined in relation to right triangles with hypoteneuse equal to 1, that is just a special case where the function is easier to define. Sine (theta), for instance, is opposite over hypotenuse, where the angle on the other end of adjacent is a right angle. Even if you don't have a right angle, the functions can help you find a superposition of a right triangle on any triangle, and that can help you solve many different kinds of problems.

The laws of sines and cosines, for instance, apply to any triangle.

The solution of this equation is the value of variable 'x' for which L.H.S.= R.H.S. The given equation is: 5x+2x+5+1-x=18

6x+6=18

Adding -6 on both sides, we get

6x=12

Dividing both sides by 6, we get

x=2

Solution is x = 2.

-5.74

You record a person's height and age (time) from birth onwards.

Start by squaring both sides of the equation to get,

(sinx + cosx)2 = 0.25

Simplify the left side to get

sin2x + 2sinxcosx + cos2x = 0.25

Using the Pythagorean identity gets

2sinxcosx + 1 = 0.25

2sinxcosx = -0.75

Using the double angle formula gets

Sin(2x) = -0.75

Take the arcsin to get

2x = sin-1(-0.75)

x = sin-1(-0.75)/2

Now, a scientific calculator can be used to find the solutions.

You cannot.

Use the tangent ratio:

250*tan(62.2) = 474.1671924

250*tan(59.5) = 424.4157798

Subtracting one from the other is the height of the tower which is about 50 meters.

Basically its just where you position the views of the main object, in first angle projection, if you view the object from the left, the view is drawn to the right of the object, in third angle projection, its drawn on the viewing side.

Look at two objects, say one about a foot away, and the other about two feet away. Move your head until the objects appear to be lined up with each other.

Now, cover and uncover one eye. Repeat it a couple of times. Then do the same thing with the other eye.

Depending on which eye is dominant, in one case the two objects will stay lined up, and in the other case they will appear to move with respect to each other.

That is parallax, which is simply the difference in perception between the viewpoints, in this case, the eyes.

Astronomers use parallax to measure long distances in space. They take pictures of an area of space they are interested in, wait 6 months, and take pictures of the same area of space. They compare the pictures. Most far distant stars will appear to be in the same position, so they line up the two pictures based on the far distant stars. Then they notice that some stars appear to be in different positions. They use trigonometry to measure the parallax error between the two pictures. Since they know the distance between the two observation points is about 186 million miles, and they know the angles of both observations, they have enough information to calculate distance to the star.

6-x+12 = 10x+7

6+12-7 = 10x+x

11 = 11x

x = 1

1/4

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