G.8 Special Right Triangles and Trig

Special Right Triangles

Multiple Select

Which of the following are considered special right triangles?

• 30-60-90

• 45-45-90

• 20-70-90

• 40-50-90

Multiple Choice

Find the missing side lengths.

• a = 4, b = 4
• a = 4, b = 2√2
• a = 2√2,  b = 4
• a = 4, b = 4

Multiple Choice

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

• 4√2
• 4
• 8
• 4√3

Multiple Choice

Find a.

• 3

• $$3\sqrt{3}$$

• 6

• $$\sqrt{3}$$

Multiple Choice

What is the value of y?

• $$5\sqrt[]{2}$$

• $$10$$

• $$5$$

• $$5\sqrt[]{6}$$

• $$None\ of\ these$$

Multiple Choice

What is the value of x?

• $$5\sqrt[]{2}$$

• $$10$$

• $$5$$

• $$5\sqrt[]{6}$$

• $$None\ of\ these$$

Multiple Choice

What is the value of x?

• $$7$$

• $$14\sqrt[]{3}$$

• $$14$$

• $$\frac{7\sqrt[]{3}}{2}$$ $$.$$

• $$None\ of\ these$$

Multiple Choice

What is the value of y?

• $$7$$

• $$14\sqrt[]{3}$$

• $$14$$

• $$\frac{7\sqrt[]{3}}{2}$$ $$.$$

• $$None\ of\ these$$

Math Response

What is the value of y? Value only, no y =

Type answer here

Correct Answer: 7

Deg^°

Rad

Math Response

What is the value of y? Value only, no y =

Type answer here

Correct Answer: 9

Deg^°

Rad

Match

Match the following for finding sides in a 30-60-90 right triangle.

• Short Leg

• Hypotenuse

• Long Leg

Half of the hypotenuse

Double the short leg

Short leg times square root of 3

• Half of the hypotenuse

• Double the short leg

• Short leg times square root of 3

Dropdown

In a 45-45-90 right triangle, to find the measure of a leg, you take the ​

Select answer

and ​

Select answer

by ​

Select answer

.​

Dropdown

In a 30-60-90 right triangle, to find the measure of the long leg, you take the ​​

Select answer

and ​ ​

Select answer

by ​

Select answer

.​

Match

Match the following for a 30-60-90 right triangle

• Short Leg

• Long Leg

• Hypotenuse

Opposite the 30° angle.

Opposite the 60° angle.

Opposite the right angle.

• Opposite the 30° angle.

• Opposite the 60° angle.

• Opposite the right angle.

Multiple Choice

In a 45-45-90 right triangle, how many sides are the same size?

• None

• Two

• All 3

• Depends on the triangle

Multiple Choice

Find x.

• 10

• $$10\sqrt{3}$$

• $$10\sqrt{2}$$

• 20

Multiple Choice

Find a.

• 3

• $$3\sqrt{3}$$

• 6

• $$\sqrt{3}$$

Multiple Choice

The legs of an isosceles triangle are 6 inches and the base is 8 inches. Find the area of the triangle.

• $$4\sqrt[]{5}$$

• $$8\sqrt[]{5}$$

• $$4\sqrt[]{13}$$

• $$8\sqrt[]{13}$$

Multiple Choice

Sin C

Remember SOH

• 20/29

• 21/29

• 21/20

Multiple Choice

Cos C

Remember CAH

• 20/29

• 21/29

• 21/20

Multiple Choice

Tan C

Remember TOA

• 20/29

• 21/29

• 21/20

Multiple Choice

Sin A

Remember SOH

• 20/29

• 21/29

• 20/21

Multiple Choice

Cos A

Remember CAH

• 20/29

• 21/29

• 20/21

Multiple Choice

Tan A

Remember TOA

• 20/29

• 21/29

• 20/21

Fill in the Blanks

16) Solve for x. Round to the nearest whole number.

$\tan\left(x\degree\right)=\frac{6}{10}$

Labeling

Using the theta angle measure,

find the appropriate labels for each side.

Drag labels to their correct position on the image

Adjacent

Opposite

Hypotenuse

Drag and Drop

2) What is the ratio for Sin(B)?

Sin(B) = ​

Placeholder

Drag these tiles and drop them in the correct blank above

Multiple Choice

Solve for the misssing distance

• 18.9
• 19.5
• 47
• 27.5

Multiple Choice

Which scenario describes the picture shown?

• A 5 foot ramp is 8 feet away from a building.  What is the angle that the ramp makes with the ground?
• A 5 foot ramp leans against an 8 foot structure.  What is the angle that the ramp makes with the ground?
• An 8 foot ramp leans
  against a building 5 feet away.  What angle does the ramp make with the ground?
• A 5 foot man is 8 feet away from a building.  What is the angle of elevation?

Multiple Choice

Solve for the missing angle.

• 50.5 degrees
• 12.7 degrees
• 36.9 degrees
• 72.2 degrees

Multiple Choice

Using the illustrations above, determine the horizontal line.

• x

• AC

• AB

• BC

Multiple Choice

the angle formed by a horizontal line and a line of sight to a point below

• Hypotenuse

• Adjacent

• Angle of Depression

• Angle of Elevation

Multiple Choice

the angle formed by a horizontal line and a line of sight to a point above

• Angle of Depression

• Angle of Elevation

• Angle of Situation

• Angle of Playa Hatin'

Multiple Choice

A 14 foot ladder is used to scale a 13 foot wall. At what angle of elevation must the ladder be situated in

order to reach the top of the wall?

• 68.2⁰

• 55.7⁰

• 48.6⁰

• 69.9⁰

Multiple Choice

An airplane is flying at an altitude of 15,000 feet. The angle of depression to a nearby air tower is 20 degrees. What is the distance between the plane and air tower?

• 43,857 feet

• 5,130 feet

• 15,963 feet

• 41,212 feet

Multiple Choice

A bird watcher spots an eagle in a tree at an angle of elevation of 57 degrees and is 50 feet from the base of the tree. How high off of the ground is the eagle?

• 77 feet

• 32 feet

• 42 feet

• 27 feet