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Afina-wow [57]
3 years ago
14

Solve each triangle. Round your answers to the nearest tenth.show work If possible ​

Mathematics
1 answer:
kvasek [131]3 years ago
5 0
<h2>Answer:</h2>

∠ABC = 76°

BC = 20.1

CA = 28.0

<h2>Step-by-step explanation:</h2>

Solving the triangle means finding all unknown angles and sides of the triangle.

(i) Two of the angles (∠BCA = 60° and ∠CAB  = 44°) are given. To find the third angle (∠ABC), use one of the theorems stating <em>that the sum of angles of a triangle is equal to 180°.</em>

Therefore, the sum of angles of the triangle ABC is 180°. i.e

∠ABC + ∠BCA + ∠CAB = 180°

=> ∠ABC + 60° + 44° = 180°

=> ∠ABC + 104° = 180°

=> ∠ABC = 180° - 104°

=> ∠ABC = 76°

(ii) One side (BA) of the triangle is given. To get the other sides, we use the sine rule as follows;

=> \frac{sin60}{25} = \frac{sin44}{BC} = \frac{sin76}{CA}

=> \frac{sinBCA}{BA} = \frac{sinCAB}{BC} = \frac{sinABC}{CA}

<em>Substitute the necessary values</em>

\frac{sin60}{25} = \frac{sin44}{BC} = \frac{sin76}{CA}      ---------------------(ii)

(a) To get side BC, use the first two terms of equation (ii)

\frac{sin60}{25} = \frac{sin44}{BC}

<em>Cross multiply</em>

BC x sin 60 = 25 x sin 44

BC x 0.8660 = 25 x 0.6947

0.8660 x BC = 17.3675

BC = \frac{17.3675}{0.8660}

BC = 20.05

=> BC = 20.1 to the nearest tenth

(b) To get CA, use any two terms of equation (ii). Using the first and third terms, we have;

\frac{sin60}{25} = \frac{sin76}{CA}

<em>Cross multiply</em>

CA x sin 60 = 25 x sin 76

CA x 0.8660 = 25 x 0.9703

0.8660 x CA = 24.2575

CA = \frac{24.2575}{0.8660}

CA = 28.01

=> CA = 28.0 to the nearest tenth

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