MISSING SIDE OF A RIGHT TRIANGLE WORKSHEET

1. In the right triangle shown below, find the value of 'a'.

2. In the right triangle shown below, find the value of 'c'.

3. In the right triangle shown below, find the value of 'c'.

4. In the right triangle shown below, find the value of 'b'.

5. In the right triangle shown below, find the value of 'a'.

6. In the right triangle shown below, find the value of 'b'.

7. Let a, b and c be the lengths of the sides of a right triangle. If a = 16, b = 63 and c is the length of hypotenuse, then find the value of c.

8. Let a, b and c be the lengths of the sides of a right triangle. If a = 16, c = 34 and c is the length of hypotenuse, then find the value of b.

9. Let a, b and c be the lengths of the sides of a right triangle. If b = 112, c = 3 and a is the length of hypotenuse, then find the value of a.

10. Let a, b and c be the lengths of the sides of a right triangle. If a = 7y, c = 3y and a is the length of hypotenuse, then find the value of b in terms of y.

1. Answer :

In the right triangle above, by Pythagorean Theorem,

152  =  52 + a

225  =  25 + a

Subtract 25 from both sides.

200 = a2

Take square root on both sides.

√200 = √a2

√(2 x 10 x 10) = a

10√2 = a

2. Answer :

In the right triangle above, by Pythagorean Theorem,

c= 72 + 92

c= 49 + 81

c= 130

Take square root on both sides.

c2 = √130

c = √130

3. Answer :

In the right triangle above, by Pythagorean Theorem,

c= 282 + 452

c= 784 + 2025

c= 2809

Take square root on both sides.

c = √2809

c = 53

4. Answer :

In the right triangle above, by Pythagorean Theorem,

14= 52 + b2

196 = 25 + b2

Subtract 25 from both sides.

171 = b2

171 = b2

171 = b

5. Answer :

In the right triangle above, by Pythagorean Theorem,

180= a2 + 1752

32400 = a2 + 30625

Subtract 30625 from both sides.

1775 = a2

1775 = a2

√(5 x 5 x 71) = a

5√71 = a

6. Answer :

In the right triangle above, by Pythagorean Theorem,

101= b2 + 992

10201 = b2 + 9801

Subtract 9801 from both sides.

400 = b2

√400 = b2

20 = b

7. Answer :

By Pythagorean Theorem,

c= a2 + b2

Substitute a = 16 and b = 63.

c= 162 + 632

c= 256 + 3969

c= 4225

Take square root on both sides.

c2 = √4225

c = 65

8. Answer :

By Pythagorean Theorem,

c= a2 + b2

Substitute a = 16 and c = 34.

34= 162 + b2

1156 = 256 + b2

Subtract 256 from both sides.

900 = b2

Take square root on both sides.

900 = b2

30 = b

9. Answer :

By Pythagorean Theorem,

a= b2 + c2

Substitute b = √112 and c = 3.

a= (√112)2 + 32

a= 112 + 9

a= 121

Take square root on both sides.

√a2 = √121

a = 11

10. Answer :

a= b2 + c2

(7y)= b2 + (3y)2

49y2 = b2 + 9y2

Subtract 9y2 from both sides.

40y2 = a2

Take square root on both sides.

√(40y2) = √a2

2y√10 = a

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