Finding the missing side of each right triangle?

Question

My daughter has a take home exam where she's allowed help and its also an open book test. The book does explain how to do this but it is very wordy and confusing. Could someone please explain these problems and explain how you got each answer? Thank you so much!

Find the missing side of each right triangle. Side c is the hypotenuse, and sides a and b are the legs.
1.) a=11 m, c=15 m
2.) b= √6 yd, c=4 yd

The next part is State if the three sides lengths form a right triangle:
1.) 10 cm, 49.5 cm, 50.5 cm
2.) 9 in, 12 in, 15 in
3.) 15 m, 12 m, 9m
4.) 48.5 ft, 39 ft, 32.5 ft

Answer 1

1.)The side of the right triangle is  a = 11 m, hypotenuse c = 15 m and b = ?

In a right angle triangle is (hypotenuse)^2 = (Side)^2 + (Side)^2

Substitute the values in formula

(15)^2 = (11)^2 + b^2

(15)^2 = 15*15 = 225 and (11)^2 = 11*11 = 121

225 = 121 + b^2

Subtract 121 from each side

225 - 121 = 121 + b^2 - 121

b^2 = 104                                                (Simplify)

Apply square root each side

√b^2 = √(104)

√(104) = √(4*26) = 2√(26)

b = 2√(26)

The missing side of the triangle is b = 2√(26) m.

Answer 2

2.) The side of the right triangle is b = √6 yd, hypotenuse c = 4 yd and a = ?

In a right angle triangle is (c)^2 = (a)^2 + (b)^2

Substitute the values in formula

(4)^2 = (a)^2 + (√6)^2

(4)^2 = 4*4 = 16 and (√6)^2 = √6*√6 = 6

16 = a^2 + 6

Subtract 6 from each side

16 - 6 = a^2 + 6 - 6

a^2 = 10                                               (Simplify)

Apply square root each side

√a^2 = √(10)

a = √(10)                                              (Simplify)

The missing side of the triangle is a = √(10) yd.

Answer 3

1.) Phythagoren theorem:

If a triangle is a right angle triangle then (Hypotenuse)^2 = (Side)^2 + (Side)^2

Let the sides are a  = 10 cm, b = 49.5 cm and hypotenuse c = 50.5 cm

Apply pythagoren theorem

(50.5)^2 = (10)^2 + (49.5)^2

(50.5)^2 = 2550.25, (10)^2 = 100 and (49.5)^2 = 2450.25

2550.25 = 100 + 2450.25

(Add: 100 + 2450.25 = 2550.25)

2550.25 = 2550.25

So the triangle is right angle triangle.

Answer 4

2.) Phythagoren theorem:

If a triangle is a right angle triangle then (Hypotenuse)^2 = (Side)^2 + (Side)^2

Let the sides are a = 9 in, b = 12 in and hypotenuse c = 15 in

Apply pythagoren theorem

(15)^2 = (9)^2 + (12)^2

(15)^2 = 225, 9^2 = 81 and (12)^2 = 144

225 = 81 + 144

(Add: 81 + 144 = 225)

225 = 225

So the triangle is right angle triangle.

Answer 5

3.) Phythagoren theorem:

If a triangle is a right angle triangle then (Hypotenuse)^2 = (Side)^2 + (Side)^2

Let the sides are a = 9 m, b = 12 m and hypotenuse c = 15 m

Apply pythagoren theorem

(15)^2 = (9)^2 + (12)^2

(15)^2 = 225, 9^2 = 81 and (12)^2 = 144

225 = 81 + 144

(Add: 81 + 144 = 225)

225 = 225

So the triangle is right angle triangle.

Answer 6

3.) Phythagoren theorem:

If a triangle is a right angle triangle then (Hypotenuse)^2 = (Side)^2 + (Side)^2

Let the sides are a = 32.5 ft, b = 39 ft and hypotenuse c = 48.5 ft

Apply pythagoren theorem

(48.5)^2 = (32.5)^2 + (39)^2

(48.5)^2 = 2352.25, (32.5)^2 = 1056.25 and (39)^2 = 1521

2352.25 = 1056.25 + 1521

(Add: 1056.25 + 1521 = 2577.25)

2352.25 = 2577.25

The statement is false.

The given measurements are not suitable for right angle triangle.So the triangle is not a right angle triangle.