Question

In triangle abc angle b=90 ,ab=7cm and ac-bc=1cm. Determine the value of sin c and cos c

Answer 1

Answer:

Step-by-step explanation:

ac - bc = 1

ac = bc + 1

ac² = bc²+ ab²

(bc + 1)² = bc² + 49

bc² + 1 + 2bc = bc² + 49

2bc + 1 = 49

2bc = 48

bc = 24

∴sin c = ac/ab = 24 + 1 / 7 = 25 / 7

cos c = ac / bc = 25 / 24

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Answer 2

Answer: Sin C=AB/AC=7/25

Cos C=BC/AC=24/25

Step-by-step explanation:

Given:

$\bigtriangleup ABC\ in\ which\ \angle B=90^{0}\\AB=7cm\\AC-BC=1cm$

To find: Sin C and Cos C

Concept: Using Pythagoras theorem and trigonometric functions.

Calculation:

$In\triangle\ ABC:AB=7cm\\\angle B=90^{0}\\In\ a\ right\ angled\ triangle:AC^{2}=AB^{2}+BC^{2}\\AB^{2}=AC^{2}-BC^{2}=(AC+BC)(AC-BC)\\7^{2}=49=(AC+BC)(1)\\AC+BC=49(Equation1)\\AC-BC=1(Equation 2)\\Adding\ both\ equation 1\ and\ equation2:\\2AC+50\\AC=25\\BC=AC-1=25-1=24$

Sin C=AB/AC=7/25

Cos C=BC/AC=24/25