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
100
The altitude of a right triangle is 18, one segment of the hypotenuse is 12. How long is the hypotenuse?
39
100
The length of the shorter leg of a 30°-60°-90° triangle is 3. What is the length of
the hypotenuse?
6
100
What does SOHCAHTOA stand for?
Sine = Opposite/Hypotenuse
Cosine = Adjacent/Hypotenuse
Tangent = Adjacent/Hypotenuse
100
What does it mean to solve a right triangle?
Find the measures of all the sides and angles.
200
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
200
State the equations of both geometric means theorems.
x2 = ab
Altitude Th.-the altitude is the geometric mean of the two segments of the hypotenuse.
Leg Th.- the leg of the rt. triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.
200
The length of the longer leg of a 30°-60°-90° triangle is root108. What is the length of the shorter leg?
6
200
The length of the hypotenuse of a right triangle is 18 and sine of angleA is 1/6.
What is the length of the side opposite angle A?
3
200
A right triangle has legs of 10 and 22. What are the measures of the two acute angles? Round to the nearest tenth.
24.4 and 65.6
300
With side lengths 11.2, 6.5, and 7.1 does this figure form a triangle? If so what type of triangle?
Yes, Obtuse.
300
One leg of a right triangle is x, the hypotenuse is 8 and the segment of the hypotenuse that is not adjacent to the leg x is 2. What is x and what is the length of the altitude? Give your answers in simplest radical form.
x = 4root3
Altitude = 2root3
300
The length of one leg of a 45°-45°-90° triangle is root3. What is the length of the hypotenuse?
root6
300
The length of one leg of a right triangle is equal to the length of the other leg.
What is the tangent of the angle between the hypotenuse and one of the other sides?
1
300
Right triangle NPQ has angle Q 65 degrees, QP = 10, and angle P = 90. What are the measures of the missing sides and angles? Round to the nearest tenth.
N = 25 degrees
NP = 21.4
NQ = 23.7
400
What is the value of x when the legs of a right triangle are 2x and 2x + 4, and the hypotenuse is 4x - 4?
x = 6.
400
A right triangle has a hypotenuse 2root89, and legs of 10 and 16. What is the length of the altitude? Round to the nearest tenth.
Altitude = 8.5
400
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
400
The length of the hypotenuse of a right triangle is
15 and the cosine of angleB is 1/3. What is the length of
the side adjacent to angleB?
5
400
What angle has a tangent value that is double its sine value?
60.
500
The sides of a triangle are x, x + 4, and 20. The longest side is 20. What values of x make this an acute triangle?
12 < x < 16
500
A right triangle has legs 20 and 15. What is the length of the altitude?
12
500
A 30-60-90 triangle has a longer leg with measure 8. What is the measure of the altitude?
4
500
A right triangle has one angle 64 degrees and hypotenuse 34. What are the lengths of the legs rounded to the nearest tenth?
30.6 & 14.9
500
You are looking at Taipei 101 from 1 km away while sitting on top of a building that is 100 m tall. You know that Taipei 101 is 508 m tall. What angle is your line of sight to the top of Taipei 101? Round your answer to the nearest degree.