Question

Hi there please help me on this

Answer 1

77 / 36

Explanation:

Finding the adjacent side

• WX² = VX² - VW² [Pythagorean Theorem]
• WX² = (85)² - (77)²
• WX² = 7225 - 2929
• WX = √1296
• WX = 36

Tangent of ∠X

• Opposite side / Adjacent side
• WX / VW
• 77 / 36

Answer 2

`\tan(X)=(77)/(36)`

Explanation:

First we need to find the length of side WX.

To do this, use Pythagoras' Theorem:
`a^2+b^2=c^2`

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

`\implies WX^2+77^2=85^2`

`\implies WX^2=85^2-77^2`

`\implies WX=√(85^2-77^2)`

`\implies WX=36`

Now use the Tan trig ratio:

`\tan(x)=\sf (O)/(A)`

where:

• 
  `x` is the angle
• O is the side opposite the angle
• A is the side adjacent the angle

From inspection of the triangle,

• 
  `x` = ∠X
• O = 77
• A = WX = 36

Substituting these values into the tan trig formula:

`\implies \tan(X)=(77)/(36)`

Therefore, the tangent of ∠X is
`(77)/(36)`