Name: ________________________________________________ Date: ____________________ Block: ____________

Unit 3: Right Triangles and TrigonometryTopic/Assignment I CAN statement Complete

d?Simplifying RadicalsRadicals Worksheet- page 2

1) I can recognize perfect square factors2) I can simplify radicals completely Yes No

Pythagorean TheoremPythagorean Theorem Worksheet – pages 3-4

1) I can find sides of a right triangle using Pythagorean theorem2) I can use the converse to determine if a triangle is a right triangle.

Yes No

TrigonometryTrig Worksheet – pages 5-6

1) I can apply the sine, cosine, and tangent ratios to find missing sides lengths Yes No

Solving Right TrianglesSolving Triangles Worksheet & Applications– pages 7-8

1) I can apply the inverse trig functions to find missing angle measurements.2) I can solve a triangle by finding all side lengths and all angle measurements.

Yes No

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Name: ________________________________________________ Date: ____________________ Block: ____________

Simplifying Radicals ReviewObjectives: 1) I can recognize perfect square factors

2) I can simplify radicals completely

Simplifying Radicals

Simplify the following radical expressions completely.

1) √50 7) 2√5⋅6√10 13)

3√5

2) 8) 14)

√5√18

3) √18 9) 15)

4) √27 10) √903 16) (5√6 )2

5) 11) 17) (7√2 )3

6) √13⋅√52 12) √273 18) 5√3⋅√62

Name: ________________________________________________ Date: ____________________ Block: ____________

THE PYTHAGOREAN THEOREM/CONVERSEObjectives: 1) I can find sides of a right triangle using Pythagorean Theorem.

2) I can use the converse to determine if a triangle is a right triangle.

Pythagorean Theorem

Pythagorean Triple

Simplify each:

A. (√3)(√6 ) B. (4 √3 )(4 √3 ) C. (6√5)2

Find the length of the missing side of the triangle. Leave answers in simplified radical form. A. B. C.

D. E. F.

Find the area of the triangle to the nearest tenth of a meter.

B.

You place a 12 foot ladder against a wall. If the base of the ladder is two ft. from the wall, how high up the wall does the top of the ladder reach? Draw a sketch!

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Name: ________________________________________________ Date: ____________________ Block: ____________

Pythagorean Theorem Converse:

If a2+b2=c2 , then ABC is

_____________.

If a2+b2>c2 , then ABC is

_____________.

If a2+b2<c2 , then ABC is

_____________.

Are the triangles obtuse, right, or acute?

a) b)

Can these side lengths form a triangle? Show why or why not.

a) 5, 10, 15 b) 5, 10, 10 c) 5, 4, 3 d) 5, 5, 10

If a triangle can be formed, classify each triangle as acute, obtuse, or right based on the following side lengths. FIRST: show if the 3 numbers can form a triangle. IF SO: show if it’s right obtuse or acute

a) 5, 6, 12 b) 7, 8, 9 c) 5, 12, 13

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CAN THE SIDE LENGTHS FORM A TRIANGLE? HOW DO YOU KNOW?

Name: ________________________________________________ Date: ____________________ Block: ____________

TRIGONOMETRY

Objectives: 1) I can apply the sine, cosine, and tangent ratios to find missing sides lengths

Trigonometric Ratio: the ratio of 2 sides of a right triangle. a number has special name(s) helps find a missing side or angle of a right triangle

Sine

Cosine

Tangent

S O H C A H T O A

Find the sine, cosine, and tangent of ∠P .

5

The 2 acute angles of a right triangle each have… A

C B

C

B

A

Name: ________________________________________________ Date: ____________________ Block: ____________

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Name: ________________________________________________ Date: ____________________ Block: ____________

Find the sine, cosine, and tangent of S for the first triangle and R of the second triangle. Express each value as a simplified fraction.

i) R ii)

S T

Use your calculator to find the following trig ratios (round to the nearest tenth).

= B) = C) =

Solve the following for the variable (round to the nearest tenth).

B) C)

D) E) F)

Use trigonometric ratios to find the value of the variables. Round to the nearest hundredth.

A) B)

C) D)

7

27

x

5

Name: ________________________________________________ Date: ____________________ Block: ____________

SOLVING RIGHT TRIANGLESObjectives: 1) I can apply the inverse trig functions to find missing angle measurements.

2) I can solve a triangle by finding all side lengths and all angle measurements.

RIGHT TRIANGLES HAVE: SOLVING A RIGHT MEANS: TO SOLVE, YOU MUST KNOW EITHER:

*Once you know the sine, cosine, or tangent of an acute angle, you can use a calculator to find the measure of the angle.

FOR ANY ACUTE ANGLE A:If sin A = x, then

If cos A = y, then

If tan A = z, then

If you are finding a SIDE you use ________________________.

If you are finding an ANGLE you use ______________________.

Solve the following right triangles. Round decimals to the nearest tenth.

A. B.

Find angle A Find angle BTan-1(3/2) = 56.310 Tan-1(2/3) = 33.690

C. D.

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Name: ________________________________________________ Date: ____________________ Block: ____________

Applications: 1) During its approach to Earth, the space shuttle’s glide angle changes. When the shuttle’s altitude is about 15.7 miles, its horizontal distance to the runway is about 59 miles. What is its glide angle? Round your answer to the nearest tenth.

When the space shuttle is 5 miles from the runway, its glide angels is about 19. Find the shuttle’s altitude at this point in its descent. Round your answer to the nearest tenth.

2) During a flight, a hot air balloon is observed by two persons standing at points A and B as illustrated in the diagram. The angle of elevation of point A is 28. Point A is 1.8 miles from the balloon as measure along the ground. Round answers to the nearest tenth.

What is the height, h, of the balloon?

Point B is 2.9 miles from point A. Find the angle of elevation of point B.

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