Question

In a triangle ABC two points D,E are taken on BC so that angle BAD=angle DAE=angleCAE. Determine AE if AB=5,BC=10 angle BAC=90. PLEASE HELP I NEED HELP WITHIN TEN MINS PLEASE

Answer 1

AE = 7.5

Explanation:

Since <BAC =
`90^(0)`, then;

<BAD = <DAE = <CAE =
`30^(0)` (complementary angles)

From ΔABC, applying the Pythagoras theorem to determine the length of side AC;

`/BC/^(2)` =
`/AC/^(2)` +
`/AB/^(2)`

`/10/^(2)` =
`/AC/^(2)` +
`/5/^(2)`

100 =
`/AC/^(2)` + 25

`/AC/^(2)` = 100 - 25

`/AC/^(2)` = 75

AC =
`√(75)`

Applying trigonometric function to ΔCAE,

Cos
`30^(0)` =
`(AE)/(√(75) )`

AE =
`√(75)` × Cos
`30^(0)`

= 7.5

Therefore, AE = 7.5