Question

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

Answer 1

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 * 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.

Answer 2

9514 1404 393

Answer:

44 cm

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.