Question

13 point question, Surds, geometry and Algebra. Help me please ! :( < 3

Answer 1

A) Tan
`60^0 √(3) = 1.732`

B) H = 12 unit

C) Area of triangle = 41.568 unit²

As per the data mentioned in the question,

It is given that,

Angle = 60° and value of the base of the triangle =
`4√(3)` unit

As we know that,

The value of, Tan 60°
`= √(3)`

Further, we can write it as: Tan 60° = 1.732 (As the value of
`√(3)=1.732`

Now finding the value of h:

As we know,

TanФ
`= (Perpendicular)/(Base)`

So, we can put 60 - degrees in place of the value of the angle,

We will get it as:

`Tan 60^0= (h)/(4√(3) )` (As here the value of the perpendicular is mentioned as h, and the value of the base is =
`4√(3)` unit

Further solving:

We will get it as:

`√(3) = (h)/(4√(3) )\\(√(3)) * (4√(3)) = h`

So, the value of h = 12 unit

Now calculating the area of the triangle

We know that,

Area of the triangle can be found by using formula:

Area =(1/2) × Perpendicular × Base

So, putting the value of perpendicular and base for finding the area:
We will get it:

Area
`= (1)/(2) * h * 4√(3)`

Area of the triangle:

`= (1)/(2) * 12 * 4√(3) \\= 24√(3) \\`

Hence Area of triangle = 41.568 unit²

Answer 2

A) Tan 60°
`√(3)` = 1.732

B) H = 12 unit

C) Area of triangle = 41.569 unit²

Explanation:

As shown in figure, the triangle with cone angle of 60° and base value 4
`√(3)` unit

A) Now, Tan 60° =
`√(3)`

Or, Tan 60° = 1.732

B) To find value of h

since TanФ =
`(Perpendicular)/(Base)`

So, Tan 60° =
`(h)/(4√(3) )`

`√(3)` =
`(h)/(4√(3) )`

∴(
`√(3)`) × (
`4√(3)` = h

∴ h = 12 unit

C) Area of this triangle =
`(1)/(2)` × Perpendicular × Base

=
`(1)/(2)` × h ×
`4√(3)`

∵ Perpendicular h = 12 unit

So, Area =
`(1)/(2)` × 12 ×
`4√(3)`

Hence Area of triangle = 41.569 unit²

ANSWER