Question

Find each measurement indicated round your answers to the nearest tenth. Part 1d. NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!

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Answer 1

see explanation

Explanation:

Using the Sine rule in all 3 questions

(1)

`(a)/(sinA)` =
`(b)/(sinB)` , substitute values , firstly calculating ∠ B

[ ∠ B = 180° - (78 + 49)° = 180° - 127° = 53° ]

`(a)/(sin78)` =
`(18)/(sin53)` ( cross- multiply )

a sin53° = 18 sin78° ( divide both sides by sin53° )

a =
`(18sin78)/(sin53)` ≈ 22.0 ( to the nearest tenth )

(3)

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

`(35)/(sinC)` =
`(45)/(sin134)` ( cross- multiply )

45 sinC = 35 sin134° ( divide both sides by 35 )

sinC =
`(35sin134)/(45)` , then

∠ C =
`sin^(-1)` (
`(35sin134)/(45)` ) ≈ 34.0° ( to the nearest tenth )

(5)

Calculate the measure of ∠ B

∠ B = 180° - (38 + 92)° = 180° - 130° = 50°

`(a)/(sinA)` =
`(b)/(sinB)` , substitute values

`(BC)/(sin38)` =
`(10)/(sin50)` ( cross- multiply )

BC sin50° = 10 sin38° ( divide both sides by sin50° )

BC =
`(10sin38)/(sin50)` ≈ 8.0 ( to the nearest tenth )