Question

Calculate the side lengths a and b to two decimal places.

A. a = 11.40 and b= 13.38
B. a = 11 and b = 15
C. a = 4.18 and b = 3.15
D. a = 10.92 and b= 14.52

Answer 1

A.)=24.78

B.)=26

C.)=7.33

D.)=25.44

Explanation:

A.)11.40+13.38=24.78

B.)11+15=26

C.)4.18+3.15=7.33

D.)10.92+14.52=25.44

Answer 2

D

Explanation:

Using the Sine rule to find a and b

We require to find ∠ C

∠ C = 180° - (115 + 43)° = 180° - 158° = 22°

Then

`(a)/(sinA)` =
`(c)/(sinC)` , substitute values

`(a)/(sin43)` =
`(6)/(sin22)` ( cross- multiply )

a × sin22° = 6 × sin43° ( divide both sides by sin22° )

a =
`(6sin43)/(sin22)` ≈ 10.92 ( to 2 dec. places )

---------------------------------------------------------

`(b)/(sinB)` =
`(c)/(sinC)` , that is

`(b)/(sin115)` =
`(6)/(sin22)` ( cross- multiply )

b × sin22° = 6 × sin115° ( divide both sides by sin22° )

b =
`(6sin115)/(sin22)` ≈ 14.52 ( to 2 dec. places )