Right Triangle Review

Right Triangle Unit Review

pythagorean theorem

Multiple Choice

If three sides of a right triangle are 9, 40, and 41, which side is the hypotenuse?

• 9
• 40
• 41

Multiple Choice

A triangle has side lengths:
20, 21, 28.  Is this triangle a right triangle, an acute triangle, or an obtuse triangle?

• right
• acute
• obtuse

Multiple Choice

The Pythagorean Theorem ONLY works on which triangle? 

• obtuse
• scalene
• isosceles
• right

Multiple Choice

The lengths of a triangle are given below. Is the the triangle obtuse, acute, or right?
4, 5, 6

• right
• obtuse
• acute

Multiple Choice

Which of the following is not a Pythagorean triple.

• 5, 12, 13

• 36, 77, 85

• 28, 45, 53

• 35, 45, 55

Multiple Choice

Which set of numbers may represent the lengths of the sides of a right triangle?

• {6,8,10}

• {4,7,10}

• {6,6,12}

• {5,12,16}

Multiple Choice

Acute, right, or obtuse?

• Acute
• Right
• Obtuse
• I don't know

Special Right Triangles

Multiple Choice

A 40 ft ladder is leaning against a house. The angle formed between the ladder and ground is 60 degrees. How many ft away from the house is the bottom of the ladder?

• 40

• 20

• 20√3

• 40√2

Multiple Choice

What is the perimeter of the triangle?

• 16 + 8√2

• 8 + 8√2

• 24√2

• 24

Multiple Choice

A square tablecloth has a line of embroidered flowers along the diagonal. The tablecloth is 48 in. on each side. How long is the embroidery line?  Round to the nearest inch.

• 48√2
• 68
• 34
• 24√2

Multiple Choice

Jeremy is going to show off his skateboarding ability to his Geometry class. He has a skate board ramp set up to rise from the ground at 30 degrees. If the height from the ground to the platform is 8 feet, how long is the ramp up to the top of the platform?

• 8

• 16

• $$8\sqrt{3}$$

• $$16\sqrt{3}$$

Multiple Choice

What are a and b in this 30-60-90 triangle?

• b=3.5√3 a = 7√3

• b = 7 a = 7√2

• b = 7 a = 14

• b = 7√3 a = 14√3

Multiple Choice

What are x and y in this 30-60-90 triangle?

• x = 6 y = 3√3
• x = 3√2 y = 3
• x = 3√3 y = 6
• x = 6 y = 3√2

Multiple Choice

What is the rule for a 3-60-90 triangle?

• $$x,\ x,\ x\sqrt{2}$$

• $$x,\ x\sqrt{3},\ 2x$$

Multiple Choice

What is the rule for a 45-45-90 triangle?

• $$x,\ x,\ x\sqrt{2}$$

• $$x,\ x\sqrt{3},\ 2x$$

Multiple Choice

Find the value of y.

• 11√2
• 11
• 22
• (11√2)/2

Multiple Choice

Find the value of y.

• 7
• 7√3
• 14√3
• (14√3)/3

Multiple Choice

Find the value of y.

• 8
• 4
• 2√3
• 8√3

Multiple Choice

A square has side length 95. What is the length of the diagonal of the square? Express your answer in simplest radical form.

• 134.4
• 67.2
• 95√2
• (95√2)/2

Multiple Choice

I have been given the short leg in this 30-60-90 triangle.  How do I find the length of the hypotenuse?

• Multiply 4 by 2
• Multiply 4 by √3
• Multiply 4 by √2
• Divide 4 by √3

Multiple Choice

I have been given the short leg in this 30-60-90 triangle.  How do I find the long leg?

• Multiply 4 by 2
• Multiply 4 by √3
• Multiply 4 by √2
• Divide 4 by 2

Multiple Choice

Which side is the long leg in this 30-60-90 triangle?

• 4
• u
• v

Multiple Choice

What is the length of y in this 45-45-90 triangle?

• 8√2
• 4√2
• 4
• 8

Multiple Choice

I have been given a hypotenuse in this 45-45-90 triangle.  How do I find the length of a leg of the triangle?

• Multiply by √2
• Divide by √2
• It's the same length as the hypotenuse.
• Divide by 2

Multiple Choice

What is the length of x in this 45-45-90 triangle?

• 4√2
• 4
• 8
• 4√3

Multiple Choice

In this 45-45-90 triangle, I have been given the length of a leg.  How do I find the length of the hypotenuse?

• It is the same length as the given leg.
• Multiply that leg's length by √2.
• Multiply that leg's length by 2.
• Divide that leg's length by √2.

Multiple Choice

In this 45-45-90 triangle, I have been given a leg, so to find the other leg I...

• Multiply that leg by 2
• Use the same length for the second leg
• Multiply that leg by √2
• Divide that leg by √2

Multiple Choice

Find x.

• 12
• √2
• √3
• 6

Multiple Choice

Find x.

• 10
• 20
• 10√3
• √3

Multiple Choice

Find x.

• 4
• 2
• √3
• 2√2

Multiple Choice

Find x.

• 10
• √3
• 5
• 10√3

Multiple Choice

What type of special triangle is this?

• 45°-45°-90°
• 30°-60°-90°
• Isosceles
• Obtuse

Multiple Choice

What type of special triangle is this?

• 45°-45°-90°
• 30°-60°-90°
• Equiangular
• Equilateral

Trig

Multiple Choice

A 16 foot ladder leans against a building.  If the angle the ladder makes with the ground is 68°, how high up the building does the ladder reach?

• 39.6
• 6.0
• 14.8
• 13.6

Multiple Choice

A yacht is anchored 90 feet offshore from the base of a lighthouse.  The angle of elevation from the boat to the top of the lighthouse is 26 degrees.  The distance between the yacht and the top of the lighthouse is about 100 feet.  Which of these is nearest to the height of the lighthouse? 

• 25 feet
• 45 feet 
• 110 feet 
• 135 feet 

Multiple Choice

A hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree.  The hawk swoops down toward the mouse at an angle of 30 degrees. What is the distance from the tree branch to the mouse? 

• 7.5 ft 
• 15 ft 
• 26 ft 
• 30 ft 

Multiple Choice

Susan is flying a kite, which gets caught in the top of a tree.  Use the diagram to estimate the height of the tree. 

• 63 ft
• 65 ft
• 74 ft
• 87 ft

Multiple Choice

What is the value of x?

• 42.59
• 0.03
• 38.60
• 8.39

Multiple Choice

What is the value of x?

• 17.30
• 11.33
• 0.06
• 23.82

Multiple Choice

If you are given the two sides that are not the hypotenuse, which trig function should you use?

• sine
• cosine
• tangent
• cotangent

Multiple Choice

Fill in the blank...
SOH ___ TOA

• COH
• CAH
• COA
• CHA

Multiple Choice

Which trigonometric ratio is correct?

• cosC= adj/hyp
• sinC= adj/hyp
• tanC= adj/hyp
• tanC=adj/opp

Multiple Choice

Triangle XYZ has right angle Y. If  $$\cos Z=\frac{5}{13}$$  , what is the decimal value of tan X.  (Hint: Draw a picture and label)

• 0.4167

• 2.4

• 0.3846

• 2.6

• 1.0833

Multiple Choice

The hypotenuse of right triangle ABC has a measure of 15 cm. Given that $$m\angle A=30\degree$$ . What is the approximate measure of the leg opposite to  $$\angle A$$  . 

• 15

• 7.5

• 7.5√3

• 30

Multiple Choice

In the figures shown below, triangle ABC is similar to triangle XYZ. What is the value of sin(B)?

• 4/5

• 3/5

• 5/3

• 5/4