In ΔJKL, the measure of ∠L=90°, JL = 24, LK = 7, and KJ = 25. What is the value of the sine of ∠K to the nearest hundredth?

sin K = 0.96

Step-by-step explanation:

Draw this triangle.  It becomes evident that the hypotenuse, JK, is 25, and we are told that LK = 7.  Side JL is 24.  We can (but do not have to) verify that 7² + 24² = 25².

Then sin K = opp / hyp = 24 / 25.  This comes out to 0.96, to the nearest hundredth.  (Actually, there's no rounding off yet, not until we determine the value of K.  On a calculator, type in arctan 0.96.  This is the desired "value of the sine of angle K to the nearest hundredth."

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).