Find x rounded to one decimal place.

as you can see you have a right angle and and a 30 degree angle. that means the last angle is a 60 degree angle. what you are going to do now is look at the other right triangle. you will have the same 60 degree angle there. and that angle is opposite to the side=2 and the hypotenuse of that right triangle is x. so its basic trig identities. sin(60)=2/x
which means
x=2/sin(60)

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erinna erinna · Answer 2 · 2021-10-19T11:02:57+02:00

The value of [tex]x[/tex] is 2.3.

Given:

The figure of a right-angle triangle.

To find:

The value of [tex]x[/tex].

Explanation:

Let us mark the vertices as shown in the attached figure.

In triangle ABD,

[tex]\sin \theta=\dfrac{\text{Perpendicular}}{\text{Hypotenuse}}[/tex]

[tex]\sin A=\dfrac{BD}{AB}[/tex]

[tex]\sin 30^\circ=\dfrac{2}{AB}[/tex]

[tex]\dfrac{1}{2}=\dfrac{2}{AB}[/tex]

On cross multiplication, we get

[tex]AB=4[/tex]

In triangle ABC,

[tex]\tan \theta=\dfrac{\text{Perpendicular}}{\text{Base}}[/tex]

[tex]\tan A=\dfrac{BC}{AB}[/tex]

[tex]\tan 30^\circ=\dfrac{x}{4}[/tex]

[tex]\dfrac{1}{\sqrt{3}}=\dfrac{x}{4}[/tex]

[tex]\dfrac{4}{\sqrt{3}}=x[/tex]

[tex]x\approx 2.3[/tex]

Therefore, the value of [tex]x[/tex] is 2.3.

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