Question

Please help me I’m stuck

Answer 1

Explanation:

use Pythagoras's theorem to find the hypontenuse of the isosceles triangle on the right side.

hyp = sqrt [ 5^2 + 5^2 ]

hyp = sqrt [ 50 ]

hyp = 7.0710678

now we know the adjacent side of the triangle on the left , since it's the same as the hypotenuse of the triangle on the right.

SOH CAH TOA ( to remember how the trig funct. fit on triangles)

CAH Cos(Ф) = adj / hyp

cos(Ф) = 7.0710678 / 8

Ф = arcCos( 7.0710678 / 8 )

Ф = 27.8855668°

TOA Tan(Ф) = x / 7.0710678

Tan( 27.8855668° ) = x / 7.0710678

7.0710678 * Tan( 27.8855668° ) = x

3.741657 = x

x = 3.7 ( to the nearest 10th )

Answer 2

`x = 3.7`

Explanation:

We can find the side of the hypotenuse by applying pythagorean theorem.

`{5}^(2) + {5}^(2) = {x}^(2)`

`25 + 25 = {x}^(2)`

`50 = {x}^(2)`

`x = 5 √(2)`

Now we can apply pythagorean theorem on the other triangle

`(5 √(2) ) {}^(2) + {x}^(2) = {8}^(2)`

`50 + {x}^(2) = 64`

`{x}^(2) = 14`

`x = √(14)`

`x = 3.7`