How to find an angle of a triangle with sides b=12 a=8 c=5 (right triangle)?

How to find an angle of a right triangle with sides b=12 a=8 c=5 what is the formula that i need to use? Thanks so much

How to find an angle of a triangle with sides b=12 a=8 c=5 (right triangle)?
.5base * height


b mustbe hypotenuse (longest side)


.5(8)(5) = 20 sq. units
Reply:Law of cosines:


(the variables are interchangeable)





A^2 = B^2 + C^2 - 2BCcos(c)


where little c is the angle opposite of the side C.





That works for any triangle, not sure if its easier because its right.
Reply:Using trigonometric ratios, one way is to take the inverse sine of : side opposite the angle divided by the hypotenuse.


so: sin^-1 (b/c) if b is opposite the angle
Reply:I don't think a right triangle is possible with those measurements. I may be wrong.





Use the trigonomic ratios
Reply:use sin cos or tan


sohcahtoa


sin=opposite/hypotinuse cos=adjacent/hypotinuse tan=opposite/adjacent
Reply:30-60-90
Reply:doesn't make much sense... since in a trianble A^2 + B^2 = C^2 and u got








12^2 = 8^2 + 5^2 = %26gt; 144 =64 + 25 so what u got is 144 = 89





that does not make much sense.





In a regular right triangle, use Tangent to find the angles...
Reply:sin 90/5 = sin X/8





cross multiply.


and for the other angle, whatever the answer is for the formula above, add it to 90 then do 180 minus that answer.
Reply:inverse tangent of the side opposite the hypotenuese divided by the side adjacent the hypoteneuse. You can use any trig function actually, inverse sine of opposite over hypotenuese, or inverse cosine of the opposite over the hypotenuese.
Reply:i think its d(squared)= a(squared)+b(squared)+c(squared)





d(squared)=64+144+25


d(squared)=233


d=15. something
Reply:i dont think this is a right angled triangle.


side b (hypotinuse) is too big.
Reply:if your in geometry, use SIN COS and TAN (all the -1st power versions).
Reply:well, since it's a right triangle, you know that one angle is 90 degrees. SInce a triangles degrees when added together equal 180 degrees the two other angles must equal 90 degrees when added together.


Sorry about that gibber jabber. Similar figures





PLANE TRIGONOMETRY is based on the fact of similar figures. (Topic 1: Ratio and proportion.) We saw:





Figures are similar if they are equiangular


and the sides that make the equal angles


are proportional.





For triangles to be similar, however, it is sufficient that they be equiangular. (Theorem 15 of "Some Theorems of Plane Geometry.") From that it follows:





Right triangles will be similar if an acute angle of one


is equal to an acute angle of the other.


Similar right triangles





In the right triangles ABC, DEF, if the acute angle at B is equal to the acute angle at E, then those triangles will be similar. Therefore the sides that make the equal angles will be proportional. If CA is half of AB, for example, then FD will also be half of DE.





Now a trigonometric Table is a table of ratios of sides. In the Table, each value of sin θ represents the ratio of the opposite side to the hypotenuse -- in every right triangle with that acute angle.





If angle θ is 28°, say, then in every right triangle with a 28° angle, its sides will be in the same ratio. We read in the Table,





sin 28° = .469





This means that in a right triangle having an acute angle of 28°, its opposite side is 469 thousandths of the hypotenuse, which is to say, a little less than half.





It is in this sense that in a right triangle, the trigonometric ratios -- the sine, the cosine, and so on -- are "functions" of the acute angle. They depend only on the acute angle.





Example. Indirect measurement. Trigonometry is used typically to measure things that we cannot measure directly.


Flagpole.





For example, to measure the height h of a flagpole, we could measure a distance of, say, 100 feet from its base. From that point P, we could then measure the angle required to sight the top . If that angle (called the angle of elevation) turned out to be 37°, then


so that h


100 = tan 37°


so that


so that h = 100 × tan 37°.





From the Table, we find





tan 37° = .754





Therefore, on multiplying by 100,





h = 75.4 feet.





(Skill in Arithmetic: Multiplying and dividing by powers of 10.)





All functions from one function





If we know the value of any one trigonometric function, then -- with the aid of the Pythagorean theorem -- we can find the rest.


Example 1. In a right triangle, sin θ = 5


13 . Sketch the triangle, place





the ratio numbers, and evaluate the remaining functions of θ.


5-12-? triangle





To find the unknown side x, we have





x² + 5² = 13²





x² = 169 − 25 = 144





Therefore,





x = = 12. (Topic 2: Radicals.)





We can now evaluate all six functions of θ:


sin θ = 5


13 csc θ = 13


5


cos θ = 12


13 sec θ = 13


12


tan θ = 5


12 cot θ = 12


5





Example 2. In a right triangle, sec θ = 4. Sketch the triangle, place the ratio numbers, and evaluate the remaining functions of θ.


4-1-? triangle





To say that sec θ = 4, is to say that the hypotenuse is


to the adjacent side in the ratio 4 : 1. (4 = 4


1 )





To find the unknown side x, we have





x² + 1² = 4²





x² = 16 − 1 = 15.





Therefore,





x = .





We can now evaluate all six functions of θ:


sin θ =


4 csc θ = 4


cos θ = 1


4 sec θ = 4


tan θ = cot θ = 1


Problem 1. In a right triangle, cos θ = 2


5 . Sketch the triangle and





evaluate sin θ.





To see the answer, pass your mouse over the colored area.


To cover the answer again, click "Refresh" ("Reload").





Problem 2. cot θ = . Sketch the triangle and evaluate csc θ.





Complements





Two angles are called complements of one another if together they equal a right angle. Thus the complement of 60° is 30°. This is the degree system of measurement in which a full circle, made up of four right angles at the center, is called 360°. (But see Topic 14: Radian Measure.)





Problem 3. Name the complement of each angle.





a) 70° 20° b) 20° 70° c) 45° 45° d) θ 90° − θ





A right triangle





The point about complements is that, in a right triangle, the two acute angles are complementary. For, the three angles of the right triangle are together equal to two right angles (Theorem 9); therefore, the two acute angles together will equal one right angle.





(When we come to radian measure, we will see that 90° = π


2 , and


therefore the complement of θ is π


2 − θ.)





Cofunctions





There are three pairs of cofunctions:





The sine and the cosine





The secant and the cosecant





The tangent and the cotangent





And here is the significance of a cofunction:





A function of any angle is equal to the cofunction


of its complement.





This means that sin 80°, for example, will equal cos 10°.





The cosine is the cofunction of the sine. And 10° is the complement of 80°.





Problem 4. Answer in terms of cofunctions.





a) cos 5° = sin 85° b) tan 60° = cot 30° c) csc 12° = sec 78°





d) sin (90° − θ) = cos θ e) cot θ = tan (90° − θ)





In the figure:


sin θ = a


c cos φ = a


c





Thus the sine of θ is equal to the cosine of its complement.


sec θ = c


b csc φ = c


b


tan θ = a


b cot φ = a


b





hope that was helpful. actually not quite sure if thats right.
Reply:if the triangle is a right triangle that means 1 side is 90 degrees... hopefully u already know this... all triangles equal 180 degrees... meaning all the angles added up... so u either have a 30, 60 right triangle or a 45, 45 right triangle but for it to be 45, 45 the triangle has to have two congruent sides so i would go with 30 and 60 degrees. hope u learned something.
Reply:It depends which angle you want to find. You first have to label the sides of the triangle. The side opposite the right angle is the longest side, and is called "hypotenuse". The side opposite the angle you want to find is called "opposite". The remaining side, next to your angle is called "adjacent". Then you can use a trigonometry forula. If you call your angle "A", you can use sine A = opposite/hypotenuse (which means the sine of A is 12 divided by whichever number (8 or 5) is the side opposite the angle you want to know. You'll then need a calculator to find the inverse sine to find the angle, A. I hope that helps.
Reply:hmm.....


| \ %26lt;-- angle c


|...\


|....\


|.....\


|____\ %26lt;---angle a





the right angle is angle b





now you know that side b is the biggest, therefore it corresponds to the right angle because that angle is the biggest.





So you cross multiply to figure out the other angles





12 (side b) ... 8 (side a)


_________ x _________


90 (angle b) ... X (angle a)





[excuse the "..." they wont let me put in spaces]





12X= 720





X= 720/12





X=60





then do the same for the other angle.