IXL - Solve a special right triangle (Geometry practice)

Solve the right triangle.

45°

Write your answers in simplified, rationalized form. Do not round.

∠

ref_doc_title.

Learn with an example

question

Solve the right triangle.

30°

Write your answers in simplified, rationalized form. Do not round.

∠

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

sin

30°

To calculate

sin

30°

first draw the 30°-60°-90° special right triangle.

30°

Calculate

sin

30°

sin

30°

Definition of sine

opp

hyp

Definition of sine

Plug in

opp

and

hyp

Plug in

opp

and

hyp

So,

sin

30°

Find

Use the definition of sine

(

sin

)

to write an equation, then solve for

sin

30°

Given

Substitute

sin

30°

Substitute

sin

30°

Multiply both sides by

Multiply both sides by 2

Simplify

So,

Find

Use the Pythagorean theorem to find

Pythagorean Theorem

Plug in

and

Plug in

and

Square

200

Square

Subtract 50 from both sides

150

Subtract 50 from both sides

Take the square root of both sides

150

Take the square root of both sides

Simplify

So,

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°

∠

30°

Plug in

∠

30°

90°

Plug in

∠

30°

∠

Subtract 30° from both sides

60°

Subtract 30° from both sides

So,

∠

60°

To summarize,

and

∠

60°

Looking for more? Try these:

Lesson: Solving right triangles

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Not feeling ready yet? These can help:

Q.5Special right triangles

Q.6Find trigonometric functions of special angles

Lesson: Solving right triangles

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