Question

Find cos α and sin β.

Answer 1

We are given a geometric figure with two right-angled triangles and asked to find:

cos α (in triangle PQR)

sin β (in triangle PRS)

Step 1: Triangle PQR

PQ = 16, PR = 20, RS = 21, QR = ?, 

Use Pythagoras’ Theorem to find QR:

PR² = PQ² + QR²

= 20² = 16² + QR²

= 400 = 256 + QR²

= QR² = 400 − 256

= QR² = 144

= QR² `sqrt144` = 12

` cos α = "adjacent side to α"/"hypotenuse" = (QR)/(PR) = 12/20 = 3/5`

Step 2: △PRS

Use Pythagoras’ Theorem to find RS:

PS² = PR² + RS²

PS² = 20² + 21²

PS² = 400 + 441

PS² = 441 + 400 

PS2 = 841

PS = `sqrt841` = 29

`sin β = "opposite"/"hypotenuse" = (PR)/(PS) = 20/29`