(1) find mn to the nearest tenth
(2) in triangle tuv below, find m
!

1. 64.0

2. 88°

Step-by-step explanation:

1. By the cosine rule,

2. Use the cosine rule,

(1) NM = 64

(2) m∠T = 87.7°

Step-by-step explanation:

(1) By using cos Rule

∵ (NM)² = (ML)² + (NL)² - 2(ML)(NL)cosL

∴ (NM)² = (47)² + (36)² - 2(47)(36)cos100

∴ (NM)² = 4092.625433

∴ NM = 63.97 ≅ 64

(2) By using cos Rule:

∵

∴

∴m∠T=

∴ m∠T = 87.7°

answer: - (a)

(b) 88 seats

step-by-step explanation:

given: in an auditorium, there are 22 seats in the first row and 28 seats in the second row.

thus first term=

second term=

the number of seats in a row continues to increase by 6 with each additional row.

⇒d= 6

a) given formula :

b)   let the number of seats (n) = 12

substitute n=12 in the explicit rule formed in (a)

∴there are 88 seats in 12 rows.