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
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Fill in the blank!: "Cotangent is the (blank) of tangent!"
reciprocal
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A triangle with side lengths of 15, 20, and 25 is (acute, right or obtuse?!)...
Right!
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Secant is the reciprocal of...
...cosine!
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
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An equilateral triangle has side lengths of 13! What is the altitude of the triangle?!
7 root 3 over 2!
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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!
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The length of the hypotenuse of a special scalene right triangle is 30. What is the length of the long leg?!
15 root 3!
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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!
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What is the area of a 30-60-90 right triangle with a long leg of 36 in simplest radical form?
216 root 3
The length of one leg of a 45°-45°-90° triangle is root3. What is the length of the hypotenuse?
root6
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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!
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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!
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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!
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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
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An equilateral triangle has an area of 512 root 3 feet. What is the measure of its base?
32 root 2 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
**RANDOM DOUBLE! 1000 POINTS!!
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!