Pythagorean Theorem
What is the equation of the Pythagorean Theorem?
a2+b2=c2
How are the side lengths of a 45˚-45˚-90˚ triangle related?
x : x : x square root 2
What is the square root of 121?
11
What is the definition of cosine?
cos(theta) = Adjacent / Hypotenuse
Inverse cos or cos^-1
If the hypotenuse has a length of 25 and one leg has the length of 7, what is the length of the other leg?
The length is 24.
How are the side lengths of a 30˚-60˚-90˚ triangle related?
x : x square root 3 : 2x
Simplify the square root of 50
5 square root 2
tan(H) = 4 / 3
For angle X, if O = 20, and H = 35, what is the measure of angle X?
34.8˚
The side lengths of a triangle are 15, 20, and 25. Is this triangle a right triangle?
Yes by the converse of the Pythagorean Theorem.
If the hypotenuse of 45˚-45˚-90˚ triangle is 10, what are the legs of the triangle?
5 square root of 2
Simplify the square root of 300
10 square root 3
For angle F, the sides are A = 15 , O = 8, and H = 17. What is tan(F)?
tan(F) = 8 / 15
For angle C, if A = 6 and H = 15, what is the measure of angle C?
66.4˚
The side lengths of a triangle are 0.3, 0.4, and 0.6. Does this make a right triangle?
No, the Pythagorean Theorem does not work.
If the leg opposite of the 60˚ side has length 9, what are the lengths of the other two sides?
3 square root 3, 6 square root 3.
Simplify the square root of 98
7 square root 2
For angle T, if A = 3, O = 4, then what is cos(T)?
cos(T) = 3 / 5
For angle B, A = 16, O = 30, H = 34, what is the measure of angle B?
61.9˚
If the length of the hypotenuse is 5 square root 6 and the length of one leg is 10 , what is the length of the other leg?
5 square root 2 or square root of 50.
If the hypotenuse of a 30˚-60˚-90˚ triangle is 18, what are the lengths of the other two sides?
9, 9 square root 3.
Simplify square root of 96
4 square root 6
For angle L, if A = 6 and O = 8, what is sin(L)?
sin(L) = 8 / 10 or 4 / 5
For angle W, A = 6, O = 8, H = 10, what is the measure of angle W?
53.1˚