Question

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

Answer 1

Answer:

$VW = 6$

$WX = 2\sqrt{3}$

$\angle V = 30$

Step-by-step explanation:

Given

$VX = 4\sqrt{3$

$\angle X = 60^\circ$

See attachment for right triangle

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

$\angle V = 180 - 90 - \angle X$

$\angle V = 180 - 90 - 60$

$\angle V = 30$