Special Right Triangles
Pythagorean Theorem
Right Triangles
Unknown Parts of a Right Triangle
Finding Trig Ratios
100

One leg of a 45-45-90 triangle measures 2. What is the lengths of the other two sides?

2 and 2 square root of 2

100

The two legs of a right triangle are 3 and 4. What is the hypotenuse?

5

100

One of the angles in a right triangle is 35 degrees. What is the measures of the other two angles?

90 and 55 degrees

100

What is the opposite/hypotenuse?

Sine of an angle

100
A= 3; O = 4; H = 5. What is the Sine ratio?
4/5
200

The short leg of a 30-60-90 triangle measures 4. What is the length of the other sides?

8 and 4 square root of 3

200

Would the following measures create a right triangle? 9, 12, 15

Yes

200

What is the longest side of a right triangle called?

Hypotenuse 

200
Right triangle ABC: leg AB=18 leg BC=12. Find angle A.
33.7
200
A = 6; O = 4; H = square root of 52. What is the tangent ratio?
2/3
300

The hypotenuse on a 45-45-90 triangle measures 6. What is the length of the legs?

3 square root of 2

300

The hypotenuse of a triangle is 5 and one of the legs is 2. What is the length of the other leg?

square root of 21

300
A triangle has three angles, where Angle 1=8x, Angle 2=x, and Angle 3=9x. What is the biggest angle of the three?

90˚

300
Right triangle KLM: Angle M=40, Hypotenuse=8, Angle L=90. Find KL.
5.1
300

You are standing on a footbridge in a city park that is 12 feet high above a pond. You look down and see a duck in the water 7 feet away from the footbridge. What is the angle of depression (The angle looking down from the eyesight to the duck).

59.7 degrees

400

The long leg of a 30-60-90 triangle measures 9. what is the length of the other two sides?

3 square roots of 3 and 6 square root of 3

400

The length of two sides of a right triangle are 8. What is the measure of the last side?

8 square root of 2

400

Explain how to tell which side is adjacent to an angle.

It the side of the angle that is touching the angle and is not the hypotenuse.

400
Right triangle RST: Angle R=50, Angle S=90, ST=15. Find the missing angle and the hypotenuse RT.
Angle S=40 and RT=17.9
400

A soccer ball is placed 10 feet away from the goal, which is 8 feet high. You kick the ball and it hits the crossbar along the top of the goal. What is the angle of elevation of your kick?

38.7 degrees

500

The hypotenuse of a 30-60-90 triangle measures 10 square root of 3. What are the lengths of the other two sides?

5 square root of 3 and 15

500

The hypotenuse of a triangle measures 5 square roots of 2 and one leg measures 4. What is the length of the other leg?

Square root of 34

500

Describe how to find the opposite side of an angle.

It is the side of the triangle that does not intersect the vertex of the angle. It is furthest away from the angle.

500
Right Triangle GHJ: Hypotenuse GJ=16, and leg GH=14. Find HJ, angle G and angle J.
angle G=29, angle J=61, HJ=7.7
500

When do you use the trigonometric ratio to find a side length of a right triangle and when to use the Pythagorean Theorem? Explain.

Trigonometric Ratios-know the sides of side length and an acute angle, use these to find other side lengths and angle measures. Pythagorean Theorem- when given two side lengths and find the third side length.

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