Right Triangles and Trigonometry

Is it a triangle?

100

Decide if the following sides are a triangle:

5, 4, 11

No

5+4 < 11

200

Decide if the following sides are a triangle:

8, 14, 9

Yes 

8 +9 >14

8 + 14 >9

9+14>8

300

Decide if the following sides are a triangle:

12, 5, 8

Yes

400

Find the range of the missing side

2, 4, x

2<x<6

500

Find the range of the missing side

18, 6, x

12<x<24

What type of triangle is it?

100

What type of triangle do the following sides make (obtuse, acute, or right)?

6, 8, 13

Obtuse

13²>6²+8²

200

What type of triangle do the following sides make (obtuse, acute, or right)?

5, 12, 13

Right 

13²=12²+5²

300

What type of triangle do the following sides make (obtuse, acute, or right)?

9, 5, 10

Acute

10²<9²+5²

400

What type of triangle do the following sides make (obtuse, acute, or right)?

27, 15, 10

Not a triangle

15+10<27

500

How do I know whether it is an obtuse, acute, or right triangle?

Pythagorean Inequalities

or

c²>a²+b²   -Obtuse

c^2<a²+b²    -Acute

c²⁼a²+b²    -Right

Find the missing side

100

In triangle ABC, angle C is the right angle. If angle A is 47 degrees and the hypotenuse is 14.142m what is the measure of side AC.

AC = 9.64m

200

In triangle ABC, angle C is the right angle. Angle B is 57 degrees and AC is 42mm. What is AB?

AB = 50.08

300

In triangle ABC, angle C is the right angle. Side AB is 57 and AC is 39. What is BC?

BC=41.57 or 18sqrt(3)

400

In triangle ABC, angle C is the right angle. Side AC is 14 and BC is 11. What is AB?

AB=17.8

**The Square root cannot reduce (317)

500

When do I use SOHCAHTOA vs. Pythagorean Theorem to solve for a missing side?

I use Pythagorean Theorem when I am given two sides and need to find the missing one. 

I use SOHCAHTOA when I have an angle and a side and need to find a missing side.

Find the missing angle

100

In triangle ABC, angle C is the right angle. If side AB=8 and AC= 4. What is angle A?

A=60

200

In triangle ABC, angle C is the right angle. Side AC is 9 and AB is 12. What is angle B?

B=48.6

300

In triangle ABC, angle C is the right angle. AC=9 and BC= 4.8. What is angle A?

A=28.07

400

In triangle ABC, angle C is the right angle. AC=9 and BC= 4.8. What is angle B? 

B = 61.92

500

When do I use inverses trig functions?

When I am given two sides and want to find an angle.

Solve the Triangle

100

In triangle XYZ angle Y is right angle. If angle X is 54 and side XY=10. Solve for the rest of the missing measures.

angle X=54, angle Y=90, XY = 10

angle Z=36

YZ=13.74

XY=17.01

200

In triangle RST, angle S is the right angle. Side SR is 5.7m long and ST is 8.4m long. Solve for the rest of the triangle.

angle S = 90, SR=5.7, ST=8.4

angle R=55.85

angle T=34.15

RT=10.15

300

If you have two angles, how can you find the third?

Subtract the two known angles from 180

400

If you are given two sides of a right triangle how can you find the third? 

Pythagorean Theorem

500

What are the four possible ways/methods to solve a right triangle?

1. Triangle sum(sum of the angles of a triangle is 180)

2. Pythagorean Theorem

3. Basic Trig

4. Inverse Trig