Using cos Law, we can easily find TU.
TU=√242+122−2∗24∗12∗cos(38)
TU ≈ 16.3127497964741677
Note: in cos(38), the 38 is in degrees, not radians.
This is a Law of Cosines problem.
Law of Cosines:
c2=a2+b2−2abcosCc=TU,a=24,b=12,C=38∘ (a and b are interchangeable, just pick one and stick with it.)TU2=242+122−2(24)(12)cos38TU2=576+144−576cos38TU2=720−576cos38TU=√720−576cos38TU≈16.3 mm
Help
Let ∠TUV=φ
tan(φ)=24⋅sin(38∘)12−24⋅cos(38∘)tan(φ)=24⋅0.6156614753312−24⋅0.78801075361tan(φ)=14.7758754078−6.91225808656|II. Quadranttan(φ)=−2.13763363908φ=−64.9294774677∘+180∘φ=115.070522532∘
TU = ?
sin(38∘)TU=sin(φ)24sin(38∘)TU=sin(115.070522532∘)24TU=24⋅sin(38∘)sin(115.070522532∘)TU=24⋅0.615661475330.90578692079TU=16.3127497965
TU≈16.3 mm