Math, asked by soni1571, 10 months ago

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

Answers

Answered by ihrishi
32

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 \\

Answered by quiratzaid456
0

Answer:

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