Answer:
BC = 11
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin45° = , then
sin 45° = =
=
=
( cross- multiply )
BC = 11
Ivan and kate live 42 miles apart. ivan leaves his house at 8:00 a.m. and bikes towards kate's house at a constant speed of 12 m
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Given that ∠B ≅ ∠C.
to prove that the sides AB = AC
This can be done by the method of contradiction.
If possible let AB =AC
Then either AB>AC or AB<AC
Case i: If AB>AC, then by triangle axiom, Angle C > angle B.
But since angle C = angle B, we get AB cannot be greater than AC
Case ii: If AB<AC, then by triangle axiom, Angle C < angle B.
But since angle C = angle B, we get AB cannot be less than AC
Conclusion:
Since AB cannot be greater than AC nor less than AC, we have only one possibility. that is AB =AC
Hence if angle B = angle C it follows that
AB = AC, and AB ≅ AC.