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 roots 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
opposite/hypotenuse
Sine
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 roots of 3
200
Would the following measures create a right triangle? 9, 12, 15
Yes
200
To solve a right triangle means to find the measures of all its ________ and ___________.
angles, sides
200

Right triangle ABC: Angle B = 90 degrees.  Angle A = 23 degrees.  leg AC = 10 . Find Leg AB

9.2

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 roots 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
What is the longest side of a right triangle called?
Hypotenuse
300
Right triangle KLM: Angle M=40, Hypotenuse=8, Angle L=90. Find KL.
5.1
300

in Triangle ABC, B is the right angle.  AB = 21, BC = 20 and AC = 29.  What is the tan(A)

20/21

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 roots of 3
400
The length of two sides of a right triangle are 8. What is the measure of the last side?
8 square roots of 2
400
Explain how to tell which side is adjacent to an angle.
It the side of the angle that is not they 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

In Right Triangle XYZ, XZ is the hypotenuse.  XZ = 37, YX = 35 and YZ = 12.  What is the cos(Z)?

12/37

500
The hypotenuse of a 30-60-90 triangle measures 10 square roots of 3. What are the lengths of the other two sides?
5 square roots 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.
500

Right Triangle GHJ: Hypotenuse GJ=14, and angle G is 44 degrees.  Find JH

9.7

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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