Question

Pls help me find all missing sides and angles. ;-;

Answer 1

see explanation

Explanation:

the sum of the 3 angles in the triangle = 180° , then

∠ BAC + 51° + 90° = 180°

∠ BAC + 141° = 180° ( subtract 141° from both sides )

∠ BAC = 39°

using the tangent ratio in the right triangle

tan51° =
`(opposite)/(adjacent )` =
`(AC)/(BC)` =
`(AC)/(12.8)` ( multiply both sides by 12.8 )

12.8 × tan51° = AC , then

AC ≈ 15.8 ( to 1 dec. place )

using the cosine ratio in the right triangle

cos51° =
`(adjacent)/(hypotenuse)` =
`(BC)/(AB)` =
`(12.8)/(AB)` ( multiply both sides by AB )

AB × cos51° = 12.8 ( divide both sides by cos51° )

AB =
`(12.8)/(cos51)` ≈ 20.3 ( to 1 dec. place )