Answer:
(a) C = 1.41
(b) D = 3.46
Step-by-step explanation:
(a)
(Im pretty sure your teacher already thought this so im skipping most of the steps, but feel free to ask in the comments)
Find C (Cosine version)
Use Formula for Cosine/Sine (You can use both of these formula because both of the angles are 45°)
Cos = [tex]\frac{adj}{hyp}[/tex]
[tex]Sin = \frac{Opp}{Hyp}[/tex]
Put the 45° with the Cos/Sin and substitute the adj and hyp with the correct values. I'll be substituting the adj with c for simplicity.
Cos45° = [tex]\frac{c}{2}[/tex]
Multiply both sides by 2 so that c can be alone
2 ⋅ Cos45° = [tex]\frac{c}{2}[/tex] ⋅ 2
= 2Cos45° = c
Flip it so that the c goes in first for it to be easier to understand
c = 2Cos45°
Put the 2Cos45° into a scientific calculator and we're done
c = 1.41
Find C (Sine Version)
Same thing with Cosine Version
Sin45° = [tex]\frac{c}{2}[/tex]
2 ⋅ Sin45° = [tex]\frac{c}{2}[/tex] ⋅ 2
c = 2Sin45°
c = 1.41
(b)
Find D
Use Formula for Sine
Sin = [tex]\frac{Opp}{Hyp}[/tex]
Put the 60° with the Sin and substitute opp and hyp with correct values. Substitute Opp with d.
Sin60° = [tex]\frac{d}{4}[/tex]
Multiply both sides by 4 so d can be alone
4 ⋅ Sin60° = [tex]\frac{d}{4}[/tex] ⋅ 4
d = 4Sin60°
d = 3.46
