Question

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 =

Answer 1

3

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

Answer 2

`y=6√(3)`.

Explanation:

It is given that,

Hypotenuse : AB=6 units.

Perpendicular : BC=y units.

`\angle BAC=30^(\circ)`

We know that, in a right angle triangle,

`\tan \theta=(Perpendicular)/(Hypotenuse)`

In triangle ABC,

`\tan A=(BC)/(AB)`

`\tan (60^\circ)=(y)/(6)`

`√(3)=(y)/(6)`
`[\because \tan (60^\circ)=√(3)]`

Multiply both sides by 6.

`6√(3)=y`

Therefore,
`y=6√(3)`.