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Use the information in the diagram to determine the height of the tree to the nearest foot.


Question 3 options:

6 ft

80 ft

72 ft

264 ft

Use the information in the diagram to determine the height of the tree to the nearest foot Question 3 options 6 ft 80 ft 72 ft 264 ft class=

Respuesta :

AlpenGlow
The answer is 80 ft. 

Based on the diagram we know that the tree triangle and the building triangle are similar triangles where the lengths of each are proportional to the other. 

The lengths of the triangle the tree makes are half of the lengths of the building triangle. So this problem can be solved using ratio and proportion:

[tex] \frac{144}{160} = \frac{72}{x} [/tex]

to solve for x, all you need to do is cross multiply then divide. 

[tex] \frac{160*72}{144} =x [/tex]

The answer is then 80ft.

Another way to solve this is just by using logic. If the lengths of the tree triangle is half of the building, simply divide the lengths of the building triangle by two. 

160ft/2 = 80ft. 

raphealnwobi

The height of the tree from the diagram is 80 ft.

Two triangles are said to be similar if the ratio of their sides are congruent.

If two angles of the triangle are the same, hence they are similar.

From the diagram, we can see that the triangle formed with the tree and the triangle formed with the building are similar. Let h represent the height of the tree, hence:

[tex]\frac{h}{160} =\frac{144}{144 + 144}\\\\ \\\frac{h}{160}=0.5\\\\\\h=80\ ft[/tex]

Therefore the height of the tree from the diagram is 80 ft.

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