Find out a if the hypotenuse is 8 cm and the base is 6 cm. Then round to one significant figure
5.2915 and 5
What is the definition of a right-angled triangle?
A triangle that has one angle equal to 90 degrees.
In a right-angled triangle, what is the side opposite the right angle called?
Hypotenuse.
If one leg of a right-angled triangle is 4 cm and the other leg is 3 cm, what is the length of the hypotenuse?
x = 5 cm.
What theorem can be used to calculate the length of the hypotenuse in a right-angled triangle?
Pythagorean theorem.
True or False: The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
True.
Fill in the blank: In a right-angled triangle with legs of length 4 cm and 3 cm, the equation is ___ + ___ = x^2.
4^2, 3^2.
What is the value of 4^2?
16.
What is the value of 3^2?
9.
Calculate x if x^2 = 16 + 9.
x = 5.
What is the formula for the Pythagorean theorem?
a^2 + b^2 = c^2.
If the lengths of the legs are a = 4 cm and b = 3 cm, what is c?
c = 5 cm.
What do the letters a, b, and c represent in the Pythagorean theorem?
a and b are the legs, c is the hypotenuse.
True or False: The hypotenuse of a right triangle is always the shortest side.
False.
If a right triangle has legs measuring 4 cm and 3 cm, what is the area?
Area = 6 cm².
How do you calculate the area of a right-angled triangle?
Area = (1/2) * base * height.
What is the base of the triangle in this problem?
4 cm.
What is the height of the triangle in this problem?
3 cm.
If the hypotenuse is 5 cm, what is the relationship between the legs and the hypotenuse?
The legs must satisfy a^2 + b^2 = 5^2.
Fill in the blank: The length of the hypotenuse can be found using the equation ___ = ___ + ___.
x^2, 4^2, 3^2.
True or False: A right triangle can have two equal legs.
True.
What is the length of the hypotenuse in a right triangle with legs of 4 cm and 4 cm?
x = 4√2 cm.
If one leg of a right triangle is doubled, what happens to the area?
The area doubles.
What happens to the hypotenuse if both legs of a right triangle are increased by 1 cm?
It increases, but not necessarily by 2 cm.
