A television is measured by its diagonal. If the height of a 70 inch television is 42 inches, what is the width?

Question

 A 10-foot ladder is leaning against a wall. The base of the ladder is 2 feet from the base of the building. How far up the building does the ladder fall?
 A television is measured by its diagonal. If the height of a 70 inch television is 42 inches, what is the width?
 An equilateral triangle has a side length of 6. What is the height of the triangle?
 A right triangle has a height of 12 and a width of 5. How long is the diagonal?
 A string is tied to the top of a plant to keep it stabilized. The plant is 5 feet tall and the string is connected to the ground 2 feet from the base of the plant. How long is the string?

Answer 1

Ashley,

 

All the eq. can be solved by Phythagoras's theorem

 

1) Diagonal is 70 inches, height is 42 inches so 

 

70^2 = 42^2 + width^2

width ^2 = 3136, width = 56 inches

 

2) Base is 2 ft, length of ladder = hypotenuse = 10 ft

 

Height^2 = 10^2 -2^2 = 96 

Height = 9.8 ft

 

3) Equilateral triangle has a side of 6

 

If you drop a vertical line from one corner of triangle to opposite side it bisects the side into equal parts. So the length of base is 3

 

The hypotenuse is 6

 

So height is sqrt (6*6 -3*3) = sqrt (27) = 3sqrt(3) = 5.2

 

4) Height = 12, width = 5 

Diagonal^2 = 12*12 + 5*5 = 169

Diagonal = 13

 

5) Plant is 5 ft tall, distance from the ground is 2 ft

 

length ^2 = 5*5 + 2*2 = 29

length = 5.38 feet