Question

Consider A RST as shown 15 cm 5 not to scale In ARST.cos R = cos. What is sin R? sin T? cos T?

Answer 1

If Cos R= (Adjacent length of R) / Hypotenuse, then the adjacent length would be 3/5 of 15, which is the hypotenuse.

3/5*15

45/5 (Multiplying)

9 (Dividing)

Using the pythagorean theorem, we have:

`\begin{gathered} a^2+b^2=c^2 \\ (9)^2+b^2=15^2\text{ (Replacing)} \\ 81+b^2=225\text{ (Raising both numbers to the power of 2)} \\ b^2=225-81\text{ (Subtracting 81 from both sides of the equation)} \\ b^2=\text{ 144 (Subtracting)} \\ b=\sqrt[]{144}\text{ (Taking the square root of both sides)} \\ b=12 \end{gathered}`

So, the opposite length of R is 12

With the lengths and the hypotenuse, we have:

sin(R)= (Opposite length of R)/(Hypotenuse)

sin(R)= 12/15 = 4/5 (Simplifying)

sin(T)= (Opposite length of T)/(Hypotenuse)

sin(T)=9/15=3/5 (Simplifying)

cos(T)=(Adjacent length of T)/(Hypotenuse)

cos(T)= 12/15 = 4/5 (Simplifying)