Pythagorean
Theorem
Theorem
Find the missing side: A right triangle has legs 4.5 and 3. What is the hypotenuse rounded to the nearest tenth?
(4.5)2 + 32 = 20.25 + 9 = 29.25
(square root 29.25) is about 5.4
The hypotenuse is 5.4.
In a 45–45–90 triangle, if one leg is 7, what is the hypotenuse?
7 * (square root 2) = 7(square root 2)
What is Mr. Lawrence's First Name?
Devin
Find sin(30 degrees).
1/2 or 0.5
Define “hypotenuse.”
The side opposite the right angle and the longest side.
A triangle has sides 5, 9.4, and (square root 113.36). Use the converse of the Pythagorean Theorem to determine if it is a right triangle.
52 + (9.4)2 = 25 + 88.36 = 113.36
(square root 113.36)2 = 113.36
113.36 = 113.36, right triangle
In a 30–60–90 triangle, the leg across from the 30 degree angle is 9. What is the length of the hypotenuse?
9 * 2 = 18
What school will Mr. Lawrence be graduating from next week?
Johns Hopkins University
In a right triangle, tan(θ) = 3/4. If the adjacent side is 8, find the opposite side.
tan is opposite/adjacent, so 3/4 relates to x/8. Multiplying 3/4 by 2/2 you get 6/8. Thus, x = 6 so the opposite side is 6.
Write each of the three trig functions as a fraction to how they correspond to their position relative to the triangle. For example, one is adjacent/hypotenuse.
sin: opposite/hypotenuse
cos: adjacent/hypotenuse
tan: opposite/adjacent
A triangle has sides 10, 15, and 18. Determine whether it is acute, right, or obtuse using the relationship among the squares of the sides.
102 + 152 = 100 + 225 = 325
182 = 324
325 > 324, acute triangle
In a 45–45–90 triangle, the hypotenuse is 10(square root 2). What is the length of each leg?
What is the best/Mr. Lawrence's favorite fast food restaurant?
Arby's
Find A if cos(A) = 3/5 to the nearest degree.
cos-1(3/5) is around 53 degrees
State the geometric mean of 4 and 9.
(square root 4 * 9) = (square root 36) = 6
A ladder leans against a wall so the bottom is 9 ft from the wall, and the ladder is 15 ft long. How high up the wall does the ladder reach?
92 + x2 = 152
81 + x2 = 225
x2 = 144
x = 12
The ladder reaches 12 feet up the wall.
A 30–60–90 triangle has hypotenuse 26. Find the longer leg. What is the degree this leg is across from?
Since the shorter side is half the hypotenuse, it would be 13. The longer leg is across from a 60 degree angle and is found by multiplying the shorter leg by (square root 3). Thus, the longer leg is 13(square root 3).
Who is the best team in the NFL (Mr. Lawrence's Favorite Team)?
The Pittsburgh Steelers
If sin(B) = 3/5 and cos(B) = 4/5, what is tan(B)?
tan(B) = sin(B)/cos(B)
tan(B) = (3/5)/(4/5)
tan(B) = 3/4
Use the Pythagorean Theorem to solve for the missing hypotenuse. a = 8 b = 15 c = x
x = 17
A triangle has side lengths x, 20, and 21, with the angle opposite side of x being a right angle. Find x. Then state whether the triangle would still be right if the side opposite the right angle were increased by 1.
202 + 212 = x2
400 + 441 = x2
841 = x2
29 = x
The side opposite of the right angle is the hypotenuse, and if it were increased by 1 c2 would increase, making it change to an obtuse triangle.
A triangle has sides 15, 15, and 15(square root 2). Verify that this is a special right triangle and determine all angle measures.
This is a 45–45–90 triangle where there are two angle measures of 45 degrees, and the 90 degree right angle.
What is the best state in the United States (Where was Mr. Lawrence born)?
New Jersey
A right triangle has a leg opposite to angle C equal to 14 and the hypotenuse equal to 20. Find angle C to the nearest degree, then find the adjacent leg to the nearest tenth.
C = sin-1(14/20) which is around 44 degrees.
142 + x2 = 202
196 + x2 = 400
x2 = 204
x is around 14.3.
What is the geometric mean of 3 & 24. KEEP YOUR ANSWER AS A RADICAL
6√2