The x- axis, y- axis and a line passing through the point A (6, 0) form a triangle ABC. If angle A=30° , then the area of the triangle, in sq.units is

Question

The x- axis, y- axis and a line passing through the point A (6, 0) form a triangle ABC. If angle A=30° , then the area of the triangle, in sq.units is (A)  6√3  (B)  12√3  (C)  4√3  (D)  8√3

Tardigrade Admin · Accepted Answer

In Δ AOB,tan 30° =(OB/OA) ⇒ (1/√3)=(OB/6) ⇒ OB=(6√3/3)=2√3 ∴ Area of Δ AOB=(1/2)× OA× OB =(1/2)× 6× 2√3=6√3 sq unit

Q. The $x -$ axis, $y -$ axis and a line passing through the point A (6, 0) form a triangle $A BC$ . If $∠ A = 30^{\circ},$ then the area of the triangle, in sq.units is

$63$

$123$

$43$

$83$

$23$

In $Δ A OB, t an 30^{\circ} = \frac{OB}{O A}$

$\Rightarrow$ $\frac{1}{3} = \frac{OB}{6}$
$\Rightarrow$ $OB = \frac{6 3}{3} = 23$
$∴$ Area of $Δ A OB = \frac{1}{2} \times O A \times OB$
$= \frac{1}{2} \times 6 \times 23 = 63$ sq unit

Q. The x− axis, y− axis and a line passing through the point A (6, 0) form a triangle ABC. If ∠A=30∘, then the area of the triangle, in sq.units is

63​

123​

43​

83​

23​

In ΔAOB,tan30∘=OAOB​ ⇒ 3​1​=6OB​ ⇒ OB=363​​=23​ ∴ Area of ΔAOB=21​×OA×OB =21​×6×23​=63​ sq unit