In ARST, r = 52 cm, s = 55 cm and ZT=48°. Find the length of t, to the nearest
centimeter.
Answers
9514 1404 393
Answer:
44 cm
Step-by-step explanation:
The law of cosines is applicable.
t^2 = r^2 + s^2 -2rs·cos(T)
t^2 = 52^2 +55^2 -2·52·55·cos(48°) ≈ 1901.57
t ≈ √1901.57 ≈ 43.607
The length of t is about 44 cm.
Hey there!
[tex]\dagger \: \sf\red{Question:}[/tex]In ARST, r = 52cm, s = 55cm and ZT = 48°. Find the length of T, to the nearest centimeter. [tex]\dagger \: \sf\blue{Solution:}[/tex]By the law of cosines,
[tex]{\underline{\boxed{\frak{\pmb{\quad {t}^{2} = {r}^{2} + {s}^{2} - 2rs \times cos(T) }}}}} [/tex][tex]\implies\tt[/tex] t² = (52)² + (55)² - 2 × 52 × 55 × cos(48°)
[tex]\implies\tt[/tex] t² ≈ 1901.57
[tex]\implies\tt[/tex] t² = √1901.57
[tex]\implies\tt[/tex] t² = 43.607
[tex]\implies\tt[/tex]t = 44 cmTherefore;
The length of t is 44 cm.Related Questions
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