How to find the angle of a triangle using son,cos tan

i cannot find it in my book..

theres a triangle ,, the hypotoneus is 5 and the opposite side is 3 and angle across the opposite side is marked A,,so i was wondering how do you find it... thanks.. :)

For finding sides, try remembering this: SOH-CAH-TOA (S = sin, C = cos, T = tan, O = opposite, A = adjacent, and H = hypotenuse)

You have an opposite side and a hypotenuse which means you have OH, the only one that has OH in it is SOH (sin).

sin angle = opposite / hypotenuse

sin A = 3 / 5

Take sin inverse (sin^(-1)): sin^(-1) (sin A) = sin^(-1) (3 / 5)

sin^(-1) and sin are inverses so they cancel out.

A = sin^(-1) (3 / 5)

Using a calculator and putting that in degrees: A = 36.87 degrees

This is how you remember the formula. SaHCoHToA. Use sin if it's adjacent over hypotenuse. Cos for opposite over hypotenuse, or tan if it's opposite over adjacent. So the formula is: depending on your calculator, press 'cos' and then divide 3 by 5 (3/5). Once you get your answer, press cos^-1 (cos to thepowerof negative 1). And that's your angle.

sin of an angle = opposite side length/hypotenuse side lenght

cos of an angle = adjacent side/hypotenuse

tan of an angle = opposite side/adjacent side

remember it like this:

SOH CAH TOA

Sin
Opposite
Hypotenuse

Cos
Adjacent
Hypotenuse

Tan
Opposite
Adjacent

sin A = 3 /5


Sin A = opposite side / hypotenuse
Cos A = adjacent side / hypotenuse
Tan A = opposite side / adjacent side

Just a different learning style.

My students preferred to make up a silly sentence to remember the SOHCAHTOA idea.

They rather liked Silly Old Harry Chased A Hippo Through Our Attic

Same idea, different way of remembering it.

The ratio of the angle A is opp/hyp = Sin angle

So Sin A = 3/5 = 0,6

A = 36,87 deg