Question

Point G is the centroid of the right △ABC with m∠C=90° and m∠B=30°. Find AG if CG=4 ft.

Answer 1

Answer:
`\text{Length of AG=}(2√(63))/(3)`

Explanation:

Please follow the diagram in attachment.

As we know median from vertex C to hypotenuse is CM

`\therefore CM=(1)/(2)AB`

We are given length of CG=4

Median divide by centroid 2:1

CG:GM=2:1

Where, CG=4

`\therefore GM=2` ft

Length of CM=4+2= 6 ft

`\therefore CM=(1)/(2)AB\Rightarrow AB=12`

In
`\triangle ABC, \angle C=90^0`

Using trigonometry ratio identities

`AC=AB\sin 30^0\Rightarrow AC=6` ft

`BC=AB\cos 30^0\Rightarrow BC=6√(3)` ft

`CN=(1)/(2)BC\Rightarrow CN=3√(3)` ft

In
`\triangle CAN, \angle C=90^0`

Using pythagoreous theorem

`AN=\sqrt{6^2+(3√(3))^2\Rightarrow √(63)`

Length of AG=2/3 AN

`\text{Length of AG=}(2√(63))/(3)` ft