IXL - Solve a triangle: mixed review (Geometry practice)

Solve the triangle.

28°

53°

Write each answer as an integer or as a decimal rounded to the nearest tenth.

∠

ref_doc_title.

Learn with an example

question

Solve the right triangle.

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

∠

key idea

The sine

(

sin

)

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

(

opp

)

divided by the length of the hypotenuse

(

hyp

)

The opposite leg is the side across from the specified angle and the hypotenuse is the side across from the right angle.

sin

(

)

opp

hyp

solution

Find

Use the Pythagorean theorem to find

Pythagorean Theorem

Plug in

and

Plug in

and

Square

Subtract 25 from both sides

Take the square root of both sides

4.898979…

Take the square root of both sides

So,

4.898979…

Find

sin

(

)

Find the sine

(

sin

)

∠

sin

(

)

Definition of sine

opp

hyp

Definition of sine

Substitute

opp

and

hyp

Substitute

opp

and

hyp

Plug in

and

Plug in

and

Divide

0.714285…

Divide

So,

sin

(

)

0.714285…

Find

∠

Use a calculator's inverse sine function

(

sin

-1

)

to find

∠

sin

(

)

Given

0.714285…

Given

sin

-1

[

sin

(

)

]

Take the inverse sine

(

sin

-1

)

of both sides

sin

-1

0.714285…

Take the inverse sine

(

sin

-1

)

of both sides

∠

Simplify

sin

-1

[

sin

(

)

]

sin

-1

0.714285…

Simplify

sin

-1

[

sin

(

)

]

∠

Find

sin

-1

0.714285…

45.584691…°

Find

sin

-1

0.714285…

So,

∠

45.584691…°

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°

∠

45.584691…°

Plug in

∠

45.584691…°

90°

Plug in

∠

45.584691…°

∠

Subtract 45.584691…° from both sides

44.415308…°

Subtract 45.584691…° from both sides

So,

∠

44.415308…°

To the nearest tenth,

≈

4.9

∠

≈

45.6°

and

∠

≈

44.4°

Looking for more? Try these:

Lesson: Solving right triangles

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R.3Solve a triangle

Q.13Solve a right triangle

Lesson: Solving right triangles

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