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Law of cosines

How to get the other angle and one side of the triangle when only the given is a=68, b=42. and beta=20. find this c=, alpha,

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For a 10ft radius octagon, how long should each side be?

There is probably a formula for this or other ways of doing this, but I will give it a shot.

An octagon has 8 sides (octopus has 8 legs). To make an octagon, we effectively have 8 triangles joined at the centre. In the centre, we have 8 equal angles. Since a full circle is 360 degrees, each of these angles must be 360 / 8 or 45 degrees.

Now we can just focus on one of these triangles. We have an angle of 45 degrees at the centre and two arms extending out 10 feet.

At this point, we can use the cosine law to calculate the length of the side or we can recognize that it is an isosceles triangle and work out the other angles and determine the length of the side.

Using Cosine Law, a^2= b^2 + c^2 - 2xbxc Cos A
In this case, A = 45 degrees, b = 10 feet, c=10 feet.

Good luck.

Let me know if you have any questions.



Aug 25, 2015 | Miscellaneous

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Final Given that Force 1 = 35 pounds and Force 2 = 120 pounds, find the angle between the forces if the magnitude of the resultant force is 140 pounds. Round answer to the nearest degree. (a)62...

You do have many math questions. If you expect us to do your homework for you, you should post under an appropriate category. I started this morning answering this question with time-consuming diagrams but did not finish and did not post the answer. During the day I tried to locate your question but for the longest time could not until I launched an all Google search over the Internet and found it. Why should anybody go through all this grief to help you? Well I just did not want my previous work to go to waste.
I hope it helps somebody.

OACB is a parallelogram. R is the resultant.
Use the cosine law in the triangle OAC
R^2=(F_1)^2+(F_2)^2 -2(F_1)(F_2) cos (angle OAC)
Replace the variables by their known values and reduce your equation to cos (angle OAC) =-53/112. Solve for angle OAC in degrees
angle OAC =arccos(-53/112). The angle between the two vectors is the supplementary of angle OAC

Dec 05, 2013 | Western Digital My Book Essential Edition...

1 Answer

How to use Texas Instruments TI34II Calculator? Especially I want to now how to use sinus, cosinus, and tangen on it. In Indonesia we call it "sin, cos, tan" Need your help, thanks.

Sinus, cosinus, and tangens (Latin names) are the same as sine, cosine, and tangent (full English names), which are abbreviated to sin, cos, and tan. If you're asking how to use these functions, they deal with right triangles and finding the missing angles or side lengths of the triangle.

Always, sine equals opposite/hypotenuse, cosine equals adjacent/hypotenuse, and tangent equals opposite/adjacent.

Using this picture, the sine of angle A equals a/c, the tangent of angle B equals b/a, and the cosine of angle A equals b/c, and so on.

In a calculator, simply hit the desired function (sin, cos, or tan), then in parenthesis put the measure of the angle, and then use what you know about the triangle to find out the rest.

Mar 03, 2011 | Texas Instruments 30XIISTKT1L1A Calculator

1 Answer

Ok so my math hw only gave me the degree, minute, sec format of the angle. How do i input it in the fx 155 es to work out and find the rest of the angles, sides, etc?

Label of key [deg symbol ' "]. It is between [(-)] and [hyp]

To enter a value in decimal degrees
12.58 [deg ' "] [=] Screen displays 12.58 deg on top line and 12 deg 34' 48" on bottom line.
Pressing the [deg ' "] key while this value is displayed will show 12.58

To enter a DMS value:

Press the [deg ' "] key after each number even if one of the numbers D,M,S is nill (0).
Exemple Enter 25 deg 0 ' 48"
25 [deg ' "] 0 [deg ' "] 48 [deg ' "] [=]
Screen displays 25 deg 0' 48" on bottom line
Pressing the [deg ' "] key converts this result to decimal degrees 25.013

This showed you how to enter angles in DMS or DD. For the rest 'find the angles, etc.' you should refer to your trigonometry manual: You have the definitions of the trigonometric ratios, the sine law, the cosine law to resolve triangles.

Feb 24, 2011 | Casio FX-115ES Scientific Calculator

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How do i use trigonometry to find out the angle in a triangle? which buttons do i press?

Sorry to say it, bu Mathematics is not Mathemagic: you cannot do things with the shaking of a wand.

There are several ways to find one angle in a right triangle when you have the measures of the sides. You must have the triangle drawn in front of you and then decide if you use the sine, the cosine or the tangent. I cannot presume to know what your triangle looks like.

I suggest you look at the definitions of the trigonometric ratios and find out what is given in your problem.

If you use a ratio to find the cosine, you can then use the arcsine function to find the angle.
If you use one particular ratio to find the sine, you can then use the arcsine to find the angle.

If you know two sides a and b and you know the angle (B) opposite side b, you can use the sine formula (sin(A)/a=sin(B)/b) to determine sin(A) then use the arcsine of the result to get angle A.

Do post a comment to this thread with the case you are trying to solve.

Nov 12, 2010 | Casio FX-9750GPlus Calculator

1 Answer

From a point on the ground, a person notices a 110-foot antenna on the top of a hill subtends an angle of 1.5 deg. If the angle of elevation on the bottom of the antenna is 25 deg, find the height of the...

Draw one right-angle triangle:

/ '
/ '
/ '

A = your location
B = bottom of the hill
C = bottom of the antenna
D = top of the antenna

The A-B distance is constant.
The B-C distance is unknown.
The B-C-D distance is unknown.
The C-D distance is given.
The C-A-B angle is given as 25 degrees.
The D-A-C angle is given as 1.5 degrees.

Use SINE and COSINE functions to determine the B-C distance.

Tell your teacher that you found the answer to your homework on the Internet.

Sep 24, 2010 | Computers & Internet

1 Answer

Find length of right triangle given one angle an one length

Formulas relating to right angled triangles are:
Sine = perpendicular divided by hypotenuse
Cosine = base divided by hypotenuse
Tangent = perpendicular divided by base
Sine Tangent and Cosine functions are all available in Excel

Aug 08, 2010 | Microsoft Excel for PC

2 Answers

What is the value of SIN15 degree and COS15 degree.....?

Hi rowanwah

The sine of an angle is only applicable is a right triangle. If you just want a number, ie, the actual value of the sine 15 degrees you can look it up on Google. Do a search for "sine and cosine functions"

If you want the mathematical description of the sine of an angle it is described as follows
In a triangle ABC, there are 3 angles angle A, angle B and angle C. There are also 3 sides, Side AB, Side AC and side BC. The sine of angle A is equal to the side opposite Angle A divided by the Hypotenuse (the longest side opposite the right angle)
The Cosine of angle A is equal to the side adjacent to Angle A divided by the hypotenuse

Hope this helps Loringh PS Please leave a rating for me Thanks

Nov 15, 2008 | Super Tutor Trigonometry (ESDTRIG) for PC

2 Answers


Hi Jehho soria

Draw a right triangle with the vertical portion of the triangle representing the 37 meters of the light house The base of the triangle is the distance we are trying to find. If the angle of depression is 15 degrees, the other angle is 75 degrees. This is the angle from the boat to the top of the lighthouse.

so The Tangent of 75 degrees is equal to the side opposite the angle (the height of the lighthouse) divided by the side adjacent (the distance we are trying to find.

solving for the distance we get distance = 37 divided by the tangent of 37 degrees

Looking up the tangent of 15 degrees on google give .2679

dividing 137 by .2679=138,1 meters

Hope this helps Loringh PS Please leave a rating for me.

Nov 14, 2008 | Super Tutor Trigonometry (ESDTRIG) for PC

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