Question

In triangle abc angle b is 90 degree and tan a is 0.75 if AC is 30 cm find the length of Ab and BC

Answer 1

Step-by-step explanation:

In triangle ABC

$\angle \: B = 90 \degree \\ tan \:A = 0.75 \\ AC = 30 \: cm \\now \: by \: pythagoras \: theorem \\ {AB}^{2} + {BC}^{2} = {AC}^{2} \\ \implies {AB}^{2} + {BC}^{2} = {30}^{2} \\ \implies {AB}^{2} + {BC}^{2} = 900....(1) \\ now \: tan \:A = \frac{BC}{AB} \\ 0.75 = \frac{BC}{AB} \: \\ \frac{75}{100} = \frac{BC}{AB} \\ \frac{3}{4} = \frac{BC}{AB} \\ \implies \: BC = \frac{3}{4}AB....(2) \\ from \: equations \: (1) \: and \: (2) \\ {AB}^{2} + {(\frac{3}{4}AB)}^{2} = 900 \: \\ {AB}^{2} + {\frac{9}{16}AB}^{2} = 900 \: \\{\frac{25}{16}AB}^{2} = 900 \\ AB^{2} = \frac{900 \times 16}{25} \\ \\ AB^{2} =36 \times 16 \\ AB = \sqrt{36 \times 16} \\ AB = 6 \times 4 \\ AB = 24 \: cm \\ \implies \: BC = \frac{3}{4}AB \\ = \frac{3}{4} \times 24 \\ = 3 \times 6 \\ = 18 \: cm \\ thus \\ AB = 24 \: cm \\ BC =18 \: cm$

Answer 2

Answer:

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