Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form. x=10/3 x=10,y=30/3 x=30.y=10/3

Use the fact that sin(x) = opp/hyp and tan(x) = opp/adj

where opp=opposite, hyp=hypotenuse, adj=adjacent and recall sin(30)=1/2 and tan(30) = 1/sqrt(3)

sin(30) = 1/2 = 17/y

y = 17(2) = 34

tan(30) = 1/sqrt(3) = 17/x  

x = 17sqrt(3)

So the answer is (d)

Note that you could have also use the Pythagorean theorem to find x instead of using tan(30).

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

the mean and mad

step-by-step explanation: