Cant work out this angle

[John]

I am given a triangle SPC

PC = 1m

SP = √2m

SC = 0.5(√5-1)

I have been asked to show was angle SCP is-

I have tried using the Cos A = (b + c - a) / 2bc formula but i can't seem to get the answer it says at the back of the book.

[Dr Maths]

What answer does the book give?

What anser did you get?

It maybe that you have not fully simplified it.

[JamesD]

Using the cos rule

cos SCP = {[0.5(√5-1)] + 1 - (√2) }/ {2[0.5(√5-1)](1)}

= [0.25(5-2√5+1) +1 -2 ] / [√5-1]

= [1.5 - 0.5√5 - 1 ] / [√5 - 1]

= [0.5 - 0.5√5] /[ √5 - 1]

= - 0.5 [√5-1] / [ √5 - 1]

= -0.5

so SCP = inv cos (- 0.5)

= 120 degrees

[John]

Thx you this website is great.

[John]

One small question how do we get from

[0.5 - 0.5√5] /[ √5 - 1]

to
- 0.5 [√5-1] / [ √5 - 1]

[Dr Math]

One small question how do we get from

[0.5 - 0.5√5] /[ √5 - 1]

to
- 0.5 [√5-1] / [ √5 - 1]

Pull out -0.5 as a common factor for convenience. It will make the numerator and denominators the same so that they can cancel.

[0.5 - 0.5√5]≡-0.5[-1 + √5] ≡- 0.5[√5 - 1 ]