Question

Find Cos α, find x, and find perimeter

Answer 1

1. x ≈ 15,73

P = 104,96

.

2. x ≈ 50,51

P = 136,26

.

3.

`\cos( \alpha ) = ( √(3) )/(3)`

P ≈ 24,88

Explanation:

1.

Use trigonometry:

`\cos(70°) = (x)/(46)`

Cross-multiply to find x:

`x = 46 * \cos(70°) ≈15.73`

In order to find the perimeter, we have to know all three side lengths of the triangle

Let's find the third one by using the Pythagorean theorem:

`{bc}^(2) = {ab}^(2) - {ac}^(2)`

`{bc}^(2) = {46}^(2) - ({15 .73})^(2) = 1868.5671`

`bc > 0`

`bc = √(1868.5671) ≈43.23`

Now, we can find the perimeter (the sum of all side lengths):

P = AB + BC + AC

P = 46 + 43,23 + 15,73 = 104,96

.

2.

`\tan(29°) = (28)/(x)`

`x = (28)/( \tan(29°) ) ≈50.51`

`{ab}^(2) = {ac}^(2) + {cb}^(2)`

`{ab}^(2) =( {50.51})^(2) + {28}^(2) = 3335.2601`

`ab > 0`

`ab = √(3335.2601) ≈57.75`

P = 57,75 + 28 + 50,51 = 136,26

.

3.

`\cos( \alpha ) = (ac)/(ab)`

`\cos( \alpha ) = (6)/(6 √(3) ) = ( √(3) )/(3)`

`p = 6 + 6 √(2) + 6 √(3) ≈24.88`