Pythagorean Theorem Basics
What does the Pythagorean theorem state?
c2=a2+b2
When using trigonometry, what letter is used to label the longest side of the right triangle?
H
When using trigonometry, what letter is used to label the side across from a reference angle?
A
How many degrees are in a triangle?
180 degrees
What mnemonic is used to describe what sides of a right triangle are associated with the trigonometric functions?
SOH CAH TOA
What letter is the hypotenuse of a right triangle typically labeled as?
c
If you are given an angle of a right triangle and the side adjacent to it, what trigonometric function should be used to find the hypotenuse?
Inverse cosine
If you are given the adjacent and opposite side of a right triangle, what trigonometric function should be used to find the angle?
Tangent
What angle does every right triangle have?
90 degrees
40 degrees
Rearrange the Pythagorean theorem to solve for side a.
a=sqrt(c^2-b^2)
A 45-45-90 triangle has a hypotenuse of 25 cm. What are the other two side lengths up to two decimal places?
17.68
The angle of elevation from 117 m away from the base of the Effiel Tower to the top of the tower is 68 degrees. What is the height of the tower up to two decimal places?
289.59 m
Triangles are classified as equilateral, isosceles, or scalene. Right triangles can be which two of these classifications?
Isosceles and scalene
What Greek letter is typically used as a label for the primary angle in a triangle?
Theta (θ)
A right triangle has a side of length 3 cm and another side of length 4 cm. If neither of these sides is the hypotenuse, calculate the missing side length without a calculator.
5 cm
An equilateral triangle has sides of length 3 cm. Calculate the height of the triangle up to two decimal places.
2.60 cm
A six-meter-long ladder leans against a wall, with the top of the ladder being four-meters above the ground. What is the angle that the ladder makes with the ground up to two decimal places?
48.19 degrees
What type of triangle is a 45-45-90 triangle?
Isosceles
What kind of right triangle is 30-60-90 triangle?
Scalene
An isosceles triangle has a base length of 10 cm. Its other two sides are 14 cm. Determine the height of the triangle up to two decimal places.
13.08 cm
An isosceles triangle has a height of 10 cm and a base b. If it has an area of 30 cm, what are the values of the two equal base angles up to two decimal places? (A=hb/2)
73.30 degrees
A right triangle has a hypotenuse of 14 m. The bottom side has a length of 6 m. Determine the two missing angles.
64.6 degrees
25 degrees
What are the side lengths of the simplest integer-sided right triangle?
3-4-5
Phi (φ)