Question
The International Space Station orbits Earth at an altitude of about 240 miles. In the
diagram, the Space Station is at point E. The radius of Earth is approximately 3,960 miles.
To the nearest ten miles, what is EH, the distance from the space station to the horizon?

The distance from the space station to the horizon is approximately
miles.

The distance from the space station to the horizon (EH) is 1399.4 miles

A circle is the locus of a point such that its distance from a fixed point is always constant.

From the diagram:

CE = CD + DE = 3960 mile + 240 mile = 4200 miles

Pythagoras theorem shows the relationship between the sides in a right angled triangle.

Using Pythagoras theorem in triangle ECH:

CE² = EH² + CH²

4200² = EH² + 3960²

EH² = 1958400

EH = 1399.4 miles

The distance from the space station to the horizon (EH) is 1399.4 miles

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Given:

CH = 3960 miles

Altitude = 240 miles

To find:

The distance from the space station to the horizon.

Solution:

The reference image for answer is attached below.

Radius = 3960 miles

CD = CH = 3960

ED = 240

EC = CD + ED

     = 3960 + 240

EC = 4200 miles

By Pythagorean theorem:

Subtract 15681600 from both sides.

Taking square root on both sides, we get

The distance from space station to the horizon is approximately 1400 miles.

answer:

step-by-step explanation:

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.