PROOF
What is the name of the longest side in a right-angled triangle?
Hypotenuse
If a right angle triangle has three sides c(H) and b and a. Solve for c if a=5, b=12.
c=13
Who is the theorem named after? And where is the person from? (Have to spell it correct)
Pythagoras, an ancient Greek mathematician.
Which ratio uses Adjacent ÷ Hypotenuse?
Cosine
State Pythagoras’ Theorem in words.
The square of the hypotenuse equals the sum of the squares of the other two sides.
If a triangle has three side c(H) and b and a. Solve for a if b=8, c=10.
a=6
About when did Pythagoras live?
Around 570–495 BCE.
True or False: Tangent = Adjacent ÷ Opposite.
False (it’s Opposite ÷ Adjacent)
If one shorter side is 6 cm, another is 8 cm, what is the hypotenuse?
10 cm
A right triangle has hypotenuse 25 and one leg 24. Find the missing side.
7
The Pythagorean Theorem can be used in 2D and 3D. Give one example of a 3D application. True or false.
True. Finding the diagonal inside a box/cube.
Which ratio would you use if you know the opposite and hypotenuse sides?
Sine
True or False: Pythagoras’ Theorem works for all triangles.
False (only for right-angled triangles).
A square field is 20 m on each side. What is the length of its diagonal?
28.28
What's Ms Zhang's puppy's name?
RayRay
A kite string is 50 m, angle with the ground is 40°. How high is the kite?
32.1 m
A triangle has sides 9, 12, and 15. Show whether it follows Pythagoras’ Theorem.
Yes, because 92+122=81+144=225=152.
A ramp rises 3 m vertically and is 12 m long. What is the horizontal distance?
What famous formula is sometimes called the “distance formula” and comes from Pythagoras’ Theorem?
(x2−x1)2+(y2−y1)2.
In a right triangle, sides are 7 (opp), 24 (adj), 25 (hyp). Which trig ratio could be used to find the angle θ ?
Any.
sinθ=7/25\sin θ = 7/25sinθ=7/25, cosθ=24/25\cos θ = 24/25cosθ=24/25, tanθ=7/24\tan θ = 7/24tanθ=7/24