Find the acute triangle Alpha
when cos 3 Alpha=- Sin 2 Aplha

Alpha is 54 degrees

Step-by-step explanation:

We can use the addition identities for cosine and for sine to express the given equation in terms of sine and cosine of alpha:

we can use the quadratic formula to find what sine of alpha is:

and for to be positive (acute angle in the first quadrant) the answer is:

99

step-by-step explanation:

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).