Question

In triangle dat, m < d = 27, m < a = 105, and t=21. find d to the nearest integer.

Answer 1

d = 13

Explanation:

Given:

m ∠ d = 27°

m ∠ a = 105°

t = 21°

Look at the picture I posted

Use sine law:

`\mathrm{( sin\:a )/( A ) = ( sin\:B )/( b )}`

∠T = 180° - 27° - 105°

∠T = 48°

`\mathrm{( sin\:48\° )/( 21 ) = ( sin\:D )/( d )}`

`\mathrm{( sin\:48\° )/( 21 ) = ( sin\:27 )/( d )}`

Cross multiply

`\mathrm{{d\:sin\:48\°} = { 21\:sin\:27\°}}`

Solve for d

`\mathrm{d = ( 21\:sin\:27\° )/( sin\:48\° )}`

Evaluate trigonometric functions in the problem

`\mathrm{d = ( 21 * 0.453990499739547 )/( 0.743144825477394 )}`

Multiply 21 and 0.453990499739547 to get 9.533800494530487

`\mathrm{d = ( 9.533800494530487 )/( 0.74314482547394 )}`

Divide 9.533800494530487 by 0.743144825477394

`\mathrm{d = 12.828993983}`

d = 13

Rounded to the nearest integer: 13