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Ede4ka [16]
3 years ago
5

In ΔABC, ∠B measures 35° and the values of a and b are 19 and 11, respectively. Find the remaining measurements of the triangle,

and round your answers to the nearest tenth. ∠A = 82.2°,∠C = 62.8°, c = 17.1 ∠A = 82.2°, ∠C = 62.8°, c = 12.4 ∠A = 22.5°, ∠C = 25.5°, c = 12.4 ∠A = 22.5°, ∠C = 25.5°, c = 17.1
Mathematics
1 answer:
Anna35 [415]3 years ago
4 0

Answer:

a)  ∠A = 82.2° , ∠C = 62.8° , c =   17.01

Step-by-step explanation:

<u><em>Explanation</em></u>:-

<u><em>Step(i)</em></u>:-

Given data ∠B measures 35° and the values of a and b are 19 and 11

∠B = 35° and sides a = 19 and b = 11

<em>By using sine rule </em>

<em></em>\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{Sin C}  = 2 R<em></em>

now we will use

\frac{a}{sin A} = \frac{b}{sin B}

\frac{19}{sin A} = \frac{11}{sin 35}

cross multiplication , we get

\frac{19 X sin 35}{11} = sinA

<em>sin A = 0.990</em>

<em>A = sin⁻¹( 0.990) = 82.2°</em>

<em> ∠A = 82.2°</em>

<u><em>Step(ii):-</em></u>

we know that ∠A +∠B +∠C = 180°

                         ∠C = 180° - ∠A -∠B

                          ∠C = 180° -82.2°-35°

                          ∠C = 62.8°

<u><em>Step(iii)</em></u>:-

<em>we will use formula</em>

<em></em>\frac{b}{sin B} = \frac{c}{Sin C}<em></em>

<em></em>\frac{11}{sin 35} = \frac{c}{Sin 62.8}<em></em>

\frac{11 X sin (62.8)}{sin 35} = C

<em>c =   17.01</em>

<u><em>Final answer</em></u>:-

<em> ∠A = 82.2° , ∠C = 62.8° , c =   17.01</em>

                         

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