Match the given conditions to the number of triangles that can be constructed from them. The lengths of the three sides are 4 centimeters, 2 centimeters, and 7 centimeters.
The measures of two angles are 30° and 60° and the length of the included side is 12 inches.
The measures of the three angles are 45°, 75°, and 60°.
Number of Triangles
Given Conditions
0
arrowBoth
1
arrowBoth
infinitely many
arrowBoth

20

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

2,160 π

step-by-step explanation:

the height of the surface increases from the center out to the sides of the road.

step-by-step explanation:

as we move out we move away from the x-axis.

and as mentioned in the problem statement that height of a road increases when we move away from the center x.

hence proved that 3rd option

the height of the surface increases from the center out to the sides of the road.

is the correct option.