Pythagorean Theorem
What are the three equations/inequalities for classifying a triangle using the converse of the Pythagorean Theorem?
a2 +b2 = c2 is right a2 + b2 < c2 is obtuse a2 + b2 > c2 is acute
A right triangle has side lengths of 3, 4 and 5 inches. What is the length of the altitude drawn from the right angle to the hypotenuse (in simplest improper fraction form!)?!
12/5
**RANDOM DOUBLE! 200 POINTS!!
A triangle with side lengths of 15, 20, and 25 is (acute, right or obtuse?!)...
Right!
An isosceles right triangle has a hypotenuse of 5 root 2 inches ! What is the measure of each leg?
5 inches!
The length of one leg of a right triangle is 1 and the length of the hypotenuse is the square root of 50. What is the length of the other leg?
7
**RANDOM DOUBLE! 400 POINTS!!
A right triangle has side lengths of 13, 12 and 5 inches. What is the length of the altitude drawn from the right angle to the hypotenuse (in simplest improper fraction form!)?!
60/13
**RANDOM DOUBLE! 400 POINTS!!
The length of the longer leg of a 30°-60°-90° triangle is root108. What is the length of the shorter leg?
6
If a figure has side lengths of 2, 6, and 3 root 5 does this figure form a triangle?! If so what type of triangle?!
Yup! Obtuse!
**RANDOM DOUBLE! 400 POINTS!!
The length of the hypotenuse of a special scalene right triangle is 30. What is the length of the long leg?!
15 root 3!
**RANDOM DOUBLE!! 600 pts!**
If a figure has side lengths of 11, 10, and 14 does this figure form a triangle? If so what type of triangle?
Yes! Acute!
A right triangle has side lengths of 12, 16 and 20 inches. What is the length of the altitude drawn from the right angle to the hypotenuse (in simplest improper fraction form!)?!
48/5
The length of one leg of a 45°-45°-90° triangle is root3. What is the length of the hypotenuse?
root6
**RANDOM DOUBLE!! 600 pts!**
The length of one leg of a right triangle is equal to the length of the other leg. If each leg has a length of root 6, what is the length of the hypotenuse (in simplest radical form!)?!
2 root 3!
If a figure has side lengths of 10, 15, and 5 root 13 does this figure form a triangle? If so what type of triangle?
Yup! Right!
If a figure has side lengths of 15, 20, and 26 does this figure form a triangle? If so what type of triangle?
Yup! Obtuse!
The long leg of a 30-60-90 triangle is 3. What are the lengths of the short leg and the hypotenuse?
Short = root 3 and Hyp = 2 root 3!
The long leg of a 30-60-90 triangle is 10. What are the lengths of the short leg and the hypotenuse?
Short leg: 10root3over3 Hypotenuse: 20root3over3
The length of the hypotenuse of a right triangle is 16 and the shortest leg of the triangle is 8, what is the area of the triangle (in simples radical form!)?!
32 root 3!
A square has a diagonal with a length of 9 root 2 m. What is the area of the square?
81 m2!
An isosceles triangle has 2 legs measuring 17 m and a base measuring 16 m. What is the area of the triangle?!
120 m2
A 30-60-90 triangle has a longer leg with measure 8 feet. What is the measure of the altitude drawn from the right angle to the hypotenuse (from the right angle to the hypotenuse!)?!
4 feet
A 30-60-90 triangle has a hypotenuse with a measure of 8 root 3. What is the area of the triangle?!
24 root 3
An isosceles triangle has 2 legs measuring 10 cm and a base measuring 12 cm. What is the height of the triangle?!
8 cm!
An equilateral triangle has 3 legs measuring 36 m. What is the area of the triangle (in simplest radical form!)?!
324 root 3 m2!