Question

Look at the picture.

Options:

A. PQ = 9.27, Area = 38.2
B. PQ = 9.267, Area = 58.2
C. PQ = 8.27, Area = 28.2
D. PQ = 7.23, Area = 42.2​

Answer 1

c

Explanation:

I think it's c I might be wrong though not sure

Answer 2

C

Explanation:

(i)

given a triangle with 2 sides and the included angle known

to find the third side use the Cosine rule

a² = b² + c² - 2bc cosA

adapting the formula to describe Δ PQR

r² = p² + q² - 2pq cosR

here r = PQ, p = QR = 7.6 , q = PR = 8.4 and ∠ R = 62° , then

r² = 7.6² + 8.4² - (2 × 7.6 × 8.4 × cos62° )

= 57.76 + 70.56 - 59.942

= 128.32 - 59.942

= 68.376 ( take square root of both sides )

r =
`√(68.378)`

≈ 8.27

that is PQ ≈ 8.27 cm ( to 2 decimal places )

(11)

the area (A) is then calculated as

A =
`(1)/(2)` pq sinR

= 0.5 × 7.6 × 8.4 × sin62°

≈ 28.2

that is area of Δ PQR ≈ 28.2 cm² ( to 1 decimal place )