# Thread: Pythagoras's theorem, sine, cosine, tangent functions

1. ## Pythagoras's theorem, sine, cosine, tangent functions

1)use Pythagoras's Theorem to find the length of the hypotenuse AB of the right angle triangle

5 sqaured = 25
9 sqaured = 81
81+25=106>sqaure root= 10.3cm?

2)use Pythagoras's to find the length of side AC on the right angled triangle

14sqaured+3sqaured=sqaure root?

3)use the Cosine rule to find the length 'x' in the triangle

4)find the angle makred '0' in the right angled triangle

5)find angles A and B in the triangle

2. ok simple
You are capable of doing question 1
so lets move onto question 2
we are given the hypotenuse and another side
since the hypotenuse is the LONGEST side of a triangle, the formula for this will be:
a^2 = c^2 - b^2

we have the lengths 14 and 3
so
x^2 = 14^2 - 3^2
= 196 - 9
= 187
x = sq. root 187

3. You have got it wrong here. Well technically since THE "cosine" rule defines a different rule altogther. Here you are using the cosine RATIO.

so cosine ratio = adj/ hyp
cos 35 = 6/ x
x = cos 35/ 6

4. we are given the opposite and adjacent here. Which means the TAN ratio
therefore:

tan x = 20/ 35
x = tan (inverse, shift + tan) of (20/35)

5. so lets find angle B first
so if we use this angle, we are given the opposite and hypotenuse
which means the SINE ratio

Sin B = 20/ 60
B = Sin (inverse) of 20/60
find that angle
then because theres 180 degrees in a triangle, you can work out the other one

(btw, when you do the inverse operations, find out the fraction first, then press shift + (whatever you need) then equals button)

3. thank but u haven't told me the answers and how do u work out the calculation on a scientific calculator