how do you figure out the angles of a triangle knowing the sides?

Acute angles of right triangles can be found based on ratios of the appropriate sides. the ratio of the opposite leg, (the height in your example) to the base is named the tangent, (abreviated tan), of the angle in question. The ratio 1/12 expressed as a decimal is .08333... Once you know the tangent of the angle the simplest way to find the angle is to use any scientific calculator. You will note these canculators have a key for sin (sine) cos (cosine), other ratios and tan. This is the one we need. Since we know the tan and not the angle we will need to fine the inverse tan of .08333.

To find the inverse of the tangent you will need to press an inverse button before you press tan. That will vary on different calculators and can be: arc, inv or 2nd. Now put in the decimal .08333. Press enter and you should have your answer in degrees. Your answer is 4.76 in degrees. (.0831 in radians, another ratio.)

Some calculators need to be put into degree mode, before you do the problem, if that is the format you want. Also some calculators require that the decimal be entered before the inverse tangent is taken. Experiment with your calculator. After a short while you should be rewarded with the correct answer.

The other acute angle is the complement of 4.76 degrees or 85.23. Incidently its tangent is 12/1 or 12. The inverse tangent of which is 85.23 degrees.

Good luck.

Peter

Base of right triangle given as 12 and height given as 1. smallest angle will be tan-1(1/12) = 4.7636 deg. The larger angle will be 90 - 4.7636 = 85.2364 deg.

if it incredibly is a staggering perspective triangle, then between the angles is ninety, and in accordance to the priority, yet another perspective is 37 we could desire to recognize the 0.33 perspective.. properly, reality: the sum of all 3 angles in a triangle is one hundred eighty (each and each time. and no count what triangle it incredibly is) consequently, the 0.33 perspective plus the different 2 upload as much as one hundred eighty (perspective) + ninety + 37 = one hundred eighty perspective = one hundred eighty - ninety - 37 perspective = fifty 3 to discover the aspects, first % any of the angles (aside from the ninety) shall we are saying we chosen 37.. the guideline says that sin(37) = (the area opposite to the perspective)/hypotenuse shall we are saying that the scale of the area opposite to the hypotenuse is x then sin(37) = x/25.5 x = (25.5)sin(37) you're able to do an identical element for the relax area by utilising the perspective we got here across above (fifty 3) yet shall we use an identical perspective yet a distinctive technique, yet another rule says: cos(37) = area adjoining to the perspective/hypotenuse permit the area adjoining to the perspective be y cos(37) = y/hypotenuse y = (25.5)cos(37) reliable success!!

If the triangle is ABC with the right angle at B, AB = 12, BC = 1, then:

tan(A) = 1/12

tan(C) = 12

You should find that A + C = 90deg.

A trick that I use is

SOH, CAH, TOA

Sine= Opposite/ Hypotnuse

Cosine= Adjacent / Hypotnuse

Tangent= Opposite/Adjacent

So if you draw your triangle and lable all your sides and angles you can fill in two of the pieces in order to find the missing piece.

There are few trigonometric formulas from which u can easily solve such type of problems.

for a triangle ABC-

sinA=height/hypo

cosA=base/hypo

tanA=height/base

so for your prob.if AB=12,BC=1then

tanA=1/12

A=inverse of tan(1/12)

A=4.76

A+C=90(as it is a rt triangle)

C=85.2

Check back in a few hours ... I'll ask my kids