Traditional Culture Encyclopedia - Photography major - In Rt△ABC, ∠BAC=90°, AB=7, AC=24, D is the height of side BC, AE is the angle bisector on BC, find the length of DE.
∵∠BAC=90°,AB=7,AC=24,
∴BC=25,
∵AD⊥BC in D,
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From t

In Rt△ABC, ∠BAC=90°, AB=7, AC=24, D is the height of side BC, AE is the angle bisector on BC, find the length of DE.
∵∠BAC=90°,AB=7,AC=24,
∴BC=25,
∵AD⊥BC in D,
p>
From t

In Rt△ABC, ∠BAC=90°, AB=7, AC=24, D is the height of side BC, AE is the angle bisector on BC, find the length of DE.

∵∠BAC=90°,AB=7,AC=24,

∴BC=25,

∵AD⊥BC in D,

From the projection theorem, AB?=BD*BC,

∴BD=49/25,

∵AE bisects ∠BAC,

∴AB/AC=BE/CE,

∴AB/(AB+AC)=BE/(BE+CE)=BE/BC

∴BE=175/31,

∴DE=BE-BD=175/31-49/25≈3.69