The moon forms a right triangle with the earth and the sun during one of its phases, as shown below:

a right angle triangle is shown with the earth at the right angle. the acute angle between the line joining the earth and the sun and the sun and the moon is x degrees. the distance between the earth and the sun is y.

a scientist measures the angle x and the distance y between the earth and the sun. using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the moon and the sun.

The scientist can calculate the distance between the moon and the sun using trigonometric ratio of Cosine.

Step-by-step explanation:

We have been given that the moon forms a right triangle with the Earth and the Sun during one of its phases.

We can see from our graph that the distance between Sun and Moon is the hypotenuse of the right triangle as it is the opposite side of right angle formed with the Earth.

The distance between Earth and Sun (y) is the adjacent side for our angle x degrees.

Since we know that the cosine of an angle is the trigonometric ratio of the adjacent side to the hypotenuse of a right triangle containing that angle.

Therefore, using trigonometric ratio Cosine, the scientist can calculate the distance between the Moon and the Sun.

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

answer: the sun

explanation:

water cycle describes the evaporation of water from earth's surface, formation of clouds and precipitation water back onto the surface of earth. seventy percent of the earth is covered with water in the form of seas and oceans. the heat of the sun causes the evaporation of water from the surface of the ocean. the water vapors rise and condense to form water droplets. the collection of these water droplets form clouds which rain down again.

the evaporation of the oceans surface water as part of the water cycle is caused by the sun