Question

7. In AABC, angleB = 90° and AC = 8 cm. If tan A = 2/3, find the lengths of the sides AB and BC.
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Answer 1

Answer:

The answer is $AB=6.654cm \: and \: BC=4.44cm$

Step-by-step explanation:

First, we can find out angle A by using information in the question.

$angle\:A=tan(\frac{2}{3})$

$angle\: A={tan}^{-1}(\frac{2}{3})$

$angle A=33.7°$

Now that we found out angle A we can use sine rule to find the length of BC.

$\frac{8}{ \sin(90) } = \frac{BC}{ \sin(33.7) }$

$BC = \frac{8 \times \sin(33.7) }{1}$

$BC=4.437cm$

After this we can calculate $AB$ using Pythagoras Theorem,

${H}^{2}={P}^{2}+{B}^{2}$

${8}^{2}={P}^{2}+{4.44}^{2}$

$64-19.7={P}^{2}$

${P}=\sqrt{44.3}$

$P=6.654cm$

And there you go! Your answer is solved. Please mark as brainliest answer, highly appreciated :)