Question

Right Triangle Trig.

Answer 1

The values are vx =
`(14√(3) )/(√(2) )`, vw =
`(14√(3) )/(√(2) )` and m∠x = 45°, for the given right angle diagram.

Explanation:

The given is,

Right angled triangle XVW,

XW = 14
`√(3)`

m∠V = 90°

m∠W = 45°

Step:1

Given diagram is right angle triangle,

Trigonometric ratios for right angle is,

`sin` ∅
`=(Opp)/(Hyp)`............................(1)

`cos` ∅
`= (Adj)/(Hyp)` .........................(2)

`tan` ∅
`= (Opp)/(Hyp)`..........................(3)

Step:2

For the value of VX,

`sin` ∅
`=(VX)/(XW)`

From given,

∅ = 45°

XW = 14
`√(3)`

Above equation becomes,

`sin` 45
`=(VX)/(14√(3) )`

Where, Sin 45 =
`(1)/(√(2) )`,

`(1)/(√(2) ) = (VX)/(14√(3) )`

`VX = (14√(3) )/(√(2) )`

Step:3

For the value of VW,

`cos` ∅
`=(VW)/(XW)`

From given,

∅ = 45°

XW = 14
`√(3)`

Above equation becomes,

`cos` 45
`=(VW)/(14√(3) )`

Where, cos 45 =
`(1)/(√(2) )`,

`(1)/(√(2) ) = (VW)/(14√(3) )`

`VW = (14√(3) )/(√(2) )`

Step:4

For the value m∠x = a,

`tan` a
`=(VX)/(VW)`

From given,

VX =
`(14√(3) )/(√(2) )`

VW =
`(14√(3) )/(√(2) )`

Above equation becomes,

`tan` a
`=\frac{(14√(3) )/(√(2) ) } {(14√(3) )/(√(2) ) }`

`tan` a = 1

a =
`tan^(-1)` (1)

a = 45°

m∠x = a = 45°

Step:5

Check for solution,

m∠v = m∠w + m∠x

= 45° + 45°

90° = 90°

Result:

The values are vx =
`(14√(3) )/(√(2) )`, vw =
`(14√(3) )/(√(2) )` and m∠x = 45°, for the given right angle diagram.