Given a right △abc, where ab = 4.5 cm, bc = 7.794 cm, and ac = 9 cm, sketch the triangle below, and find the measure m∠c in degrees, rounded to the nearest tenth, if necessary.

  30°

Step-by-step explanation:

The ratio of the side opposite (AB) to the hypotenuse (AC) is ...

  4.5/9 = 1/2

From your memory of a short table of trig functions you know this is the sine of 30°. From the mnemonic SOH CAH TOA, you know that

  Sin = Opposite/Hypotenuse

Putting these facts together gets you ...

  sin(C) = 1/2 = sin(30°)

  C = 30°

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.