You are an astronomer on planet tirth, which orbits a distant star. it has recently been accepted that tirth is spherical in shape, though no one knows its size. one day, you learn that on the equinox your sun is directly overhead in the city of tyene, located 750 kilometers due north of you. on the equinox, you go outside in alectown and observe that the altitude of your sun is 87.0 ∘.

The circumference of planet tirth is

Explanation:

From the question we are told that

   The distance of tyene from the observer is  

   The altitude of the sun from the equinox is  

Generally given that on the equinox your sun is directly overhead in the city of tyene , then the altitude of the tyene from the equinox is  

Generally the angular distance between tyene and the sun as observed from the equinox is mathematically represented as

=>      

=>      

Generally the ratio of to   which is the total angle in a circle is equal to the ratio of   to the circumference of the planet

So

=>      

=>    

emily ruth's annual premium is $1058.50

step-by-step explanation:

emily ruth is a female of 27 years age purchasing 20 year endowment insurance with face value $25000.

from the given table,

for females, the age of a male 3 years younger should be used.

so, we have to check for 24 year male for 20 year endowment.

it is 42.34 for every $1000 face value.

for a face value of $25000,

it is 25 * 42.34 = $1058.50

∴ emily ruth's annual premium is $1058.50