Question

In ARST, r = 52 cm, s = 55 cm and ZT=48°. Find the length of t, to the nearest
centimeter.

Answer 1

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.

Answer 2

Hey there!

$\dagger \: \sf\red{Question:}$

• In ARST, r = 52cm, s = 55cm and ZT = 48°. Find the length of T, to the nearest centimeter.

$\dagger \: \sf\blue{Solution:}$

By the law of cosines,

${\underline{\boxed{\frak{\pmb{\quad {t}^{2} = {r}^{2} + {s}^{2} - 2rs \times cos(T) }}}}}$

$\implies\tt$ t² = (52)² + (55)² - 2 × 52 × 55 × cos(48°)

$\implies\tt$ t² ≈ 1901.57

$\implies\tt$ t² = √1901.57

$\implies\tt$ t² = 43.607

$\implies\tt$t = 44 cm

Therefore;

• The length of t is 44 cm.