Question

Solving a right triangle ‼️ Can someone help me find B, b, and c❓Round to the nearest tenth.

Answer 1

see explanation

Explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 given angles from 180 for B

B = 180° - (90 + 39)° = 180° - 129° = 51°

Using the tangent and sine ratios in the right triangle for b and c

tan39° =
`(opposite)/(adjacent)` =
`(27)/(b)`

Multiply both sides by b

b × tan39° = 27 ( divide both sides by tan39° )

b =
`(27)/(tan39)` ≈ 7.5 ( to the nearest tenth )

sin39° =
`(opposite)/(hypotenuse)` =
`(27)/(c)`

Multiply both sides by c

c × sin39° = 27 ( divide both sides by sin39° )

c =
`(27)/(sin39)` ≈ 28.0 ( to the nearest tenth )