Right Triangles - Unit 2.3 Test Review

Special Right Triangles

1

What is the missing angle?

 45 degrees

2

What is the name of this type of special triangle?

30-60-90

3

What is the formula to find the hypotenuse in a 45-45-90 degree triangle?

 x times the square root of 2

4

What is the formula for finding the hypotenuse in a 30-60-90 degree triangle.

2x (two times x)

5

Find b and c

b=5 times square root 3

c= 10

Trig Ratios

1

What is the acronym we use to remember the basic trig ratios? HINT: sock-uh-toe-uh

*Answer must be spelled correctly*

SOHCAHTOA

2

How do we know which side is the hypotenuse?

It' across from the right angle! (Right angle points towards hypotenuse)

3

Which side is ADJACENT (ADJ) to angle b?

The side with length 3

4

Find cosX

cosX= 4/5

5

If cosβ =4/5 , what is sinα ?

sinα =4/5

Solution:

sinβ=cosα

cosβ=sinα

By the identity of sine and cosine of complementary angles

Find the Side

1

Set up an equation for sinA

sin42=x/25

2

Set up an equation we could use to solve for y

cos30=y/10

3

Find b. Round to the nearest whole number!

b =4

Solution:

tan25= b/8

8tan25 = b

3.7 = b

Rounding to the nearest whole number, 4=b

4

Find the missing opposite side length given an angle of 53 degrees and a hypotenuse of length 2.5 (Round to the nearest whole number.)

OPP=2

Solution:

sin=opp/hyp

sin53=OPP/2.5

2.5sin53=OPP

1.99 = OPP

Rounding to the nearest whole number, 2=OPP

5

Find the missing adjacent side length given an angle of 41 degrees and a hypotenuse length of 7. (Round to the nearest whole number.)

ADJ= 5

Solution:

cos= adj/hyp

cos41 =ADJ/7

7cos41 = ADJ

5.2 = ADJ

Rounding to the nearest whole number, 5=ADJ

Find the Angle

1

Which trig function would we use to find the missing angle?

sin^-1  (Inverse sine)

2

Set up the equation we would use to find the missing angle?

x = sin^-1(3/8)

3

The missing angle measurement given an opposite side length of 5 and a hypotenuse length of 10.3 (Round to the nearest whole degree)

What is 29 degrees?

4

Find the two angle measurements given the same side lengths of 3.

Both angles are 45 degrees!

This is a 45-45-90 triangle

5

Find the m∠ B. (Round to the nearest whole number)

 

m∠ B = 56

Solution:

cosB=10/18

B=cos^-1(10/18)

B=56.2

Rounding to the nearest whole number, B=56

Solving Right Triangles

1

Write the statement that shows the two smaller triangles are similar

△ JKM ∼ △ KLM

2

Find x

x=4

Solution:

short leg/short leg = long leg/long leg

x/12=12/36

36x=144

x=4

3

Let cosA = j and cosA= k. What expression represents the value of sinB - cosB?

j-k

Solution:

Draw your triangle

AB = 1

BC = k

AC = j

sinB = opp/hyp

sinB =j/1  

sinB = j

cosB =adj/hyp

cosB =k/1  

cosB = k

Thus, sinB - cosB = j - k

4

A lighthouse shines its light on a boat from a distance of 3600 meters at an 27 degree angle of depression. Approximately what is the vertical distance from the top of the lighthouse to the sea?  (Round to the nearest whole number)

HINT: Find CB

1,634 meters

Solution:

sin27=CB/3600

3600sin27=CB

1634.3=CB

Rounding to the nearest whole number, 1634=CB

5

A lighthouse shines its light on a boat from a distance of 3600 meters at an 27 degree angle of depression. Approximately what is the horizontal distance from the boat to the base of the lighthouse?  (Round to the nearest whole number)

HINT: Find AB

3,208 meters

Solution:

cos27=AB/3600

3600cos27=AB

3207.6=AB

Rounding to the nearest whole number, 3208=AB