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What is the value of y? Triangle A B C has right angle C with hypotenuse labeled 6. Angle A is 60 degrees and its opposite side B C is labeled y. Enter your answer, as an exact value, in the box. y =

What is the value of y Triangle A B C has right angle C with hypotenuse labeled 6 Angle A is 60 degrees and its opposite side B C is labeled y Enter your answer class=

Respuesta :

Answer:

[tex]y=6\sqrt{3}[/tex].

Step-by-step explanation:

It is given that,

Hypotenuse : AB=6 units.

Perpendicular : BC=y units.

[tex]\angle BAC=30^{\circ}[/tex]

We know that, in a right angle triangle,

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

In triangle ABC,

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

[tex]\tan (60^\circ)=\dfrac{y}{6}[/tex]

[tex]\sqrt{3}=\dfrac{y}{6}[/tex]     [tex][\because \tan (60^\circ)=\sqrt{3}][/tex]

Multiply both sides by 6.

[tex]6\sqrt{3}=y[/tex]

Therefore, [tex]y=6\sqrt{3}[/tex].

grantgreving1

Answer:

3

Step-by-step explanation:

you can solve this 2 different ways:

You can use the sine ratio or, since the triangle is a 30 60 90,you can solve it that way.

1:

sine 30 = opposite/hypotenuse

sin 30 = y/6

(sin 30)6 = (y/6)6

sin 30 (6) = y

y = 0.5 (6)

y = 3

2:

Since triangle ABC is a 30 60 90 triangle, the hypotenuse will always be 2 times the shorter leg:

hypotenuse = 2(shorter leg)

6 = 2y

6/2 = 2y/2

3 = y

y = 3

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