Determining the degrees on an angle on a triangle just knowing the lengths of the sides?

Question

Wanted to know if possible to do without a table of sines, cosines, etc. If it simplifies answer, than one angle may be known.

Answer 1

It is impossible to determine the angles of a triangle given the sides if trigonometric functions will not be used, i.e., the sine, cosine, and tangent functions. Because the relationship between the angles and the sides can be only found by applying trigonometry.

Answer 2

You do not need any angles, and you do not need tables either. Apply the following generalization of the Pythagorean Theorem:

LAW OF COSINES: Let a, b, and c denote the sides of a triangle, and let A be the angle opposite to a, let B be the anble opposite to b, and let C be the angle opposite to c. We will write A for the measure of angle A, etc, by agreement. Then we have

a^2 + b^2 - 2ab cos C = c^2;

b^2 + c^2 -2bc cos A = a^2;

a^2 + c^2 -2AC cos B = b^2.

As for how to calculate cosines without tables, what you really need are inverse cosines. The procedures for doing this involves Taylor expansions.

Step 1: Solve for the cosine of the angle you need, from algebra.
Step 2: Of course, you could use a table of cosines, or you could use a Taylor expansion for the arccosine function, which can be constructed about the square root of 1/2. then, you apply it, and get an answer in radians. To convert this answer to degrees, multiply it by 180/(pi).

Now, if you want to make your own table of cosines to use, here is how to do it: In radians (between 0 and pi), the formula to use is

cos x = 1 - (1/2)x^2 + (1/24)x^4 - (1/720)x^6 + (1/40320)x^8 - (1/ 3628800)x^10 +E ,

where the error E is less than .00193 in magnitude. Degrees can be converted to radians by multiplying the degrees by (pi)/180.

Of course, if you are allowed to use a scientific calculator, then the arccosine function (same as the inverse cosine function) will be available on it.

Answer 3

you cannot do anything without using cosine law or sine law and table of sines and cosines
cosine law :
cosA = (b^2 + c^2 - a^2) / 2bc
cosB = (a^2 + c^2 - b^2) / 2ac
cosC = (a^2 + b^2 - c^2) / 2ab
sine law : sinA/a = sinB/b = sinC/c

however, if the triangle is special, you can calculate the degree of the angles without knowing about sine or cosine.

So you should give an typical problem to solve, not just ask such a common question

Answer 4

use the sine law ann cosine law to find the length and angles of a triangle

Answer 5

Our chum Pythagoras solved this difficulty thousands of years in the past. He established that the sq. of the hypotenuse (area opposite the right attitude) is the sum of the squares of the legs (aspects adjoining to the right attitude). on your particular difficulty, convert both lengths to inches. [attempting to multiply and compute roots base-12 is difficult artwork.] The length of the third area [hypotenuse] is the sq. root of 26 and a million/12 ft squared plus 40 ft squared.

Answer 6

You will need to know the law of cosine.
a = sqrt(b^2 + c^2 - 2bc*cos A)

where a, b and c are the triangles sides and A is theangle opposite to side a.

Answer 7

Without using trig ratios ...... I doubt !

U can do it in one way ..... consrtuct the triangle with the given sides and the measure the angle required !

Answer 8

do not know