Question

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

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the Sine rule in all 3 questions

(1)

$\frac{a}{sinA}$ = $\frac{b}{sinB}$ , substitute values , firstly calculating ∠ B

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

$\frac{a}{sin78}$ = $\frac{18}{sin53}$ ( cross- multiply )

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

a = $\frac{18sin78}{sin53}$ ≈ 22.0 ( to the nearest tenth )

(3)

$\frac{c}{sinC}$ = $\frac{a}{sinA}$ , substitute values

$\frac{35}{sinC}$ = $\frac{45}{sin134}$ ( cross- multiply )

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

sinC = $\frac{35sin134}{45}$ , then

∠ C = $sin^{-1}$ ( $\frac{35sin134}{45}$ ) ≈ 34.0° ( to the nearest tenth )

(5)

Calculate the measure of ∠ B

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

$\frac{a}{sinA}$ = $\frac{b}{sinB}$ , substitute values

$\frac{BC}{sin38}$ = $\frac{10}{sin50}$ ( cross- multiply )

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

BC = $\frac{10sin38}{sin50}$ ≈ 8.0 ( to the nearest tenth )