PRACTICE PROBLEMS USING SPECIAL RIGHT TRIANGLES

Part 1 Questions :

(1)  Find the length of the hypotenuse in the triangle shown below. 

Solution

(2)

Solution

(3)  

Solution

(4)

Solution

(5)  The road sign is shaped like an equilateral triangle. If the length of each side is  36 inches, estimate the area of the sign by finding the area of the equilateral triangle.

Solution

Part 1 Answers :

(1)  x = 3√2

(2)  5√2/2 = x

(3)  x = 10√3/3 and s  =  5√3/3

(4)  49.5 ≈ h

(5)   561.18 square inches. 

Part 2 Questions :

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

Solution

Part 2 Answers :

1)  a  =  10 and b  =  5√3

2) a  =  8 and b  =  8√2

3)  a  =  6 and b  =  6√3

4)  a  =  3 and b  =  3

5) a  =  2√2 and b  =  4

6)  a  =  7

7)  a  =  12 and b  =  6√3

8)  a  =  8√2 and 

b  =  8√2

Part 3 Answers :

(1)  In the figure given below, find the value of x.

Solution

(2)  In the figures below, find the values of x and y.

Solution

(3) 

In the figure above, if AD  =  BD  =  2√3, what is the length of AB ?            Solution

(4)

In the figure given above AB  =  6, BC  =  8 and CD  =  5. What is the length of AD?           Solution

(5)

In the above triangle ABC,  BD  =  √3. What is the perimeter of triangle ABC.         Solution

(6)  In the triangle above, <A    <C and BD bisects AC. What is the perimeter of triangle ABC ?

Part 3 Answers :

(1)  x  =  5

(2)  x  =  3/√3 and y  =  2√3

(3)  AB  =  6

(4)  AD  =  5√3

(5)  2√3+6

(6)    2√3+6

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