IXL - Solve a right triangle (Geometry practice)

Solve the right triangle.

31°

Write your answers as integers or as decimals rounded to the nearest tenth.

∠

ref_doc_title.

Learn with an example

question

Solve the right triangle.

27°

Write your answers as integers or as decimals rounded to the nearest tenth.

∠

key idea

The cosine

(

cos

)

of an angle in a right triangle is a ratio. It is the length of the adjacent leg

(

adj

)

divided by the length of the hypotenuse

(

hyp

)

The adjacent leg is the leg next to the specified angle and the hypotenuse is the side across from the right angle.

cos

(

)

adj

hyp

solution

Find

Use the definition of cosine

(

cos

)

to write an equation, then solve for

cos

Definition of

cos

Definition of

cos

27°

Plug in

27°

and

Plug in

27°

and

0.891006…

Find

cos

27°

Find

cos

27°

0.891006…

Multiply both sides by

Divide both sides by 0.891006…

6.733957…

Divide both sides by 0.891006…

So,

6.733957…

Find

Use the Pythagorean theorem to find

Pythagorean Theorem

Plug in

and

≈

6.734

Plug in

and

≈

6.734

Square

45.3468

Square

Subtract 36 from both sides

9.3468

Subtract 36 from both sides

Take the square root of both sides

3.057253…

Take the square root of both sides

So,

3.057253…

Find

∠

and

∠

are the acute angles of a right triangle, so they are complementary. Write an equation setting the sum of their measures equal to 90°, and solve for

∠

90°

27°

∠

Plug in

∠

27°

90°

Plug in

∠

27°

∠

Subtract 27° from both sides

63°

Subtract 27° from both sides

So,

∠

63°

To the nearest tenth,

≈

6.7

≈

3.1

and

∠

63°

Looking for more? Try these:

Lesson: Solving right triangles

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Teacher tools

Work it out

Not feeling ready yet? These can help:

Q.11Trigonometric ratios: find a side length

Q.12Trigonometric ratios: find an angle measure

P.1Pythagorean theorem

DD.5Complementary and supplementary angles

Q.7Solve a special right triangle

Lesson: Solving right triangles

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