Question

in triangle ABC angel A = angel C =45° angel B = 90° 16 root 2 cm find AB =?​

Answer 1

Step-by-step explanation:

Consider ΔABD and ΔACD:

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P=\arΔABD\arΔACD=12AB⋅ADsin∠BAD12AC⋅ADsin∠CAD

P=ABsin∠BADACsin∠CAD(1)

Using the Law of Sines,

ABsin45°=ACsin60°

ABAC=sin45°sin60°=2–√3–√(2)

From (1) and (2):

P=2–√sin∠BAD3–√sin∠CAD(3)

But, because these triangles have the same altitude,

P=BDDC=13(4)

Equating (3) and (4):

2–√sin∠BAD3–√sin∠CAD=13

sin∠BADsin∠CAD=16–√