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Tema [17]
3 years ago
14

Solve the right triangle. 4 3 E F D 60° Write your answers in simplified, rationalized form. Do not round.

Mathematics
1 answer:
djyliett [7]3 years ago
7 0

Answer:

VW = 6

WX = 2\sqrt{3}

\angle V = 30

Step-by-step explanation:

Given

VX = 4\sqrt{3

\angle X = 60^\circ

<em>See attachment for right triangle</em>

Required

Solve for VW, WX and \angle V

First, calculate VW

To do this, we make use of:

sin(\theta) = \frac{Opposite}{Hypotenuse}

In this case,

sin(60) = \frac{VW}{4\sqrt{3}}

Make VW the subject

VW =  4\sqrt{3} * sin(60)

In radical form:

sin(60) = \frac{\sqrt{3}}{2}

VW =  4\sqrt{3} * \frac{\sqrt{3}}{2}

VW =  \frac{4\sqrt{3} *  \sqrt{3}}{2}

VW =  \frac{4*3}{2}

VW =  \frac{12}{2}

VW = 6

To solve for WX, we make use of Pythagoras Theorem, we make use of:

VX^2 = VW^2 + WX^2

(4\sqrt{3})^2 = 6^2 + WX^2

16*3 = 36 + WX^2

48= 36 + WX^2

Subtract 36 from both sides

48 - 36 = 36 - 36 + WX^2

48 - 36 = WX^2

12= WX^2

Take the square root of both sides

\sqrt{12}= WX

\sqrt{4*3}= WX

\sqrt{4}*\sqrt{3}= WX

2\sqrt{3}= WX

WX = 2\sqrt{3}

Solving \angle V

To do this, we make use of:

\angle V + \angle X + 90 = 180

Make V the subject

\angle V = 180 - 90 - \angle X

\angle V = 180 - 90 - 60

\angle V = 30

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