Use Trigonometric Ratios and Pythagorean Theorem to Solve Right Triangles: CCSS.Math.Content.HSG-SRT.C.8

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Geometry › Use Trigonometric Ratios and Pythagorean Theorem to Solve Right Triangles: CCSS.Math.Content.HSG-SRT.C.8

Questions 1 - 10

1

Determine whether a triangle with side lengths , , and is a right triangle.

No

Yes

Explanation

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in for , for , and for c.

If both sides are equal, then the side lengths result in a right triangle.

$\2 ^2+ 3 ^2= 6 ^2 \4 + 9 = 36 \13 = 36$

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

2

Determine whether a triangle with side lengths , , and is a right triangle.

No

Yes

Explanation

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in for , for , and for .

If both sides are equal, then the side lengths result in a right triangle.

$\1 ^2+ 2 ^2= 12 ^2 \1 + 4 = 144 \5 = 144$

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

3

Determine whether a triangle with side lengths , , and is a right triangle.

No

Yes

Explanation

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in for , for , and for .

If both sides are equal, then the side lengths result in a right triangle.

$\2 ^2+ 3 ^2= 5 ^2 \4 + 9 = 25 \13 = 25$

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

4

Determine whether a triangle with side lengths , , and is a right triangle.

No

Yes

Explanation

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in for , for , and for .

If both sides are equal, then the side lengths result in a right triangle.

$\1 ^2+ 2 ^2= 14 ^2 \1 + 4 = 196 \5 = 196$

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

5

Determine whether a triangle with side lengths , , and is a right triangle.

No

Yes

Explanation

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in for , for , and for .

If both sides are equal, then the side lengths result in a right triangle.

$\4 ^2+ 5 ^2= 11 ^2 \16 + 25 = 121 \41 = 121$

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

6

Determine whether a triangle with side lengths , , and is a right triangle.

No

Yes

Explanation

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in for , for , and for .

If both sides are equal, then the side lengths result in a right triangle.

$\1 ^2+ 2 ^2= 11 ^2 \1 + 4 = 121 \5 = 121$

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

7

Determine whether a triangle with side lengths , , and is a right triangle.

No

Yes

Explanation

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in for , for , and for .

If both sides are equal, then the side lengths result in a right triangle.

$\7 ^2+ 8 ^2= 9 ^2 \49 + 64 = 81 \113 = 81$

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

8

Determine whether a triangle with side lengths , , and is a right triangle.

No

Yes

Explanation

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in for , for , and for .

If both sides are equal, then the side lengths result in a right triangle.

$\1 ^2+ 2 ^2= 4 ^2 \1 + 4 = 16 \5 = 16$

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

9

Determine whether a triangle with side lengths , , and is a right triangle.

Yes

No

Explanation

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in for , for , and for .

If both sides are equal, then the side lengths result in a right triangle.

$\3 ^2+ 4 ^2= 5 ^2 \9 + 16 = 25 \25 = 25$

Since both sides are equal, we can conclude that the side lengths are a right triangle.

10

Determine whether a triangle with side lengths , , and is a right triangle.

No

Yes

Explanation

To figure this problem out, we need to recall the Pythagorean Theorem.

$a^{2} + b^{2} = c^{2}$

Now we simply plug in for , for , and for .

If both sides are equal, then the side lengths result in a right triangle.

$\3 ^2+ 4 ^2= 11 ^2 \9 + 16 = 121 \25 = 121$

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

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