Question

Triangle ABC has a right angle at Angle A. Cos(c) is 7/25. What is sin(c)?A. 25/26B. 7/24C. 24/25D. 7/26

Answer 1

Step 1

Write an expression for cosine and sine, using their ratios

`\begin{gathered} Co\sin e\text{ =}\frac{adjacent}{\text{hypothenuse}} \\ \sin e\text{ = }\frac{opposite\text{ }}{\text{hypothenuse}} \end{gathered}`

Step 2

Define the values of adjacent, opposite, hypothenuse

From the question Cos(c) = 7/25

Hence by comparison with the ratio above

adjacent = 7

hypothenuse = 25

Opposite =?

Step 3

Find the value of the opposite using Pythagoras theorem

Hence, from the diagram using Pythagoras theorem

`\begin{gathered} \text{hypothenuse}^2=adjacent^2+opposite^2 \\ \text{opposite}^2=hypothenuse^2-adjacent^2 \\ \text{opposite =}\sqrt[]{hypothenuse^2-adjacent^2} \\ After,\text{ substitution} \\ \text{opposite =}\sqrt[]{25^2-7^2} \\ \text{opposite = }\sqrt[]{576} \\ \text{opposite =24} \end{gathered}`

Step 4

Find the value of sine(c)

`\begin{gathered} \text{From the equation above} \\ \sin (c)\text{ = }\frac{opposite}{\text{hypothenuse}},\text{ after susbstitution} \\ \sin (c)\text{ = }(24)/(25) \end{gathered}`

Hence, sin(c) = 24/25... Option C