Yes you are right from what i seen
Begin with cos(θ) = 5/13, θ in Quadrant IV
you should distinguish the 5-12-13 right-angled triangle
and then cosØ = adjacent/hypotenuse
x = 5, r = 13 , y = -12, since Ø is in IV
and sinØ = -12/13
also tan(ϕ) = −√15 = -√15/1 = y/x and ϕ is in II,
y = √15 , x = -1
r^2 = x^2 + y^2 = 15+1 = 16
r = 4
sinϕ = √15/4 , cosϕ = -1/4
you must know that:
cos(θ − ϕ) = cosθcosϕ + sinθsinϕ
= (5/13)(-1/4) + (-12/13)(√15/4)
= -5/52 - 12√15/52
= (-5-12√15)/52
Outcome
Hope this helps :)
Répondre:
AI = 32,36 m
IE = 30,78 m
Explication étape par étape:
Utilisation de Pythagore:
Cosθ = adjacent / hypoténus
AI = hypoténus
θ = 72 °
Adjacent = 10 m
Cos 72 = 10 / AI
0,3090169 = 10 / AI
AI = 10 / 0,3090169
AI = 32,36 m
De la trigonométrie;
IE = opposé
Adjacent = 10m
Tanθ = opposé / adjacent
Tan 72 = IE / 10
IE = Tan 72 * 10
IE = 3,0776835 * 10
IE = 30,78 m