When the moon is exactly half full, the earth, moon, and sun form a right angle (see the figure). at that time the angle formed by the sun, earth, and moon (using the earth as its vertex) is measured to be 89.85°. if the distance from the earth to the moon is 240,000 mi, estimate the distance from the earth to the sun. (round your answer to one decimal place.)

  91,673,351.9 miles . . . or . . .  91.7 million miles

Step-by-step explanation:

If s represents the earth-sun distance, and m represents the earth-moon distance, then s is the hypotenuse of the right triangle with m as the leg adjacent to the given angle:

  Cos = Adjacent/Hypotenuse . . . . . . . . . from SOH CAH TOA

  cos(89.85°) = m/s

  s = m/cos(89.85°) = 240,000/0.0026179908874

  s ≈ 91,673,351.9 . . . miles

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We suspect that "round to one decimal place" means "express the answer in millions of miles, rounded to one decimal place." If that is the correct interpretation, the distance is ...

  earth to sun ≈ 91.7 million miles

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation: