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2 years ago

Find the missing term in the geometric sequence. 180,___,5

Mathematics

1 answer:

Elan Coil [88]2 years ago

7 0

Answer:

30.

Step-by-step explanation:

first term = a

3r term = ar^2

So here ar^2/ a = r^2

r^2 = 5/180 = 1/36

r = 1/6

So missing term = 180 * 1/6 = 30.

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2 years ago

What are the sine and cosine ratios for a 30°–60°–90° triangle with a hypotenuse of 6, when θ = 60°?

Margaret [11]

Answer:

There are two ways to do this problem algebraically or trigonometrically.

Algebraically/geometrically

The ratios of the sides of a 30/60/90 tri. are x, x√3, 2x (short leg, long leg, hyp). Therefore, if the long leg is 6 'units'. then 6 = x√3. x = 6√3.

The hyp is 2x then the hypotenuse is 2(6√3) = 12√3, rationalizing is 12√3/3 = 4√3

Using Trig.

We can use sinx = y/r = opp/hyp. The long leg of 6 is opposite 60 degrees (pi/3).

Therefore, sin(pi/3) = 6/r =

r = 6/sin(pi/3) = 6/(√3/2) = 12/√3, when you rationalize you get 12√3/3 = 4√3

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1 year ago