Pythagorean Theorem, Triangle Inequality Theorem and Pythagorean Triples
Special right triangles
Application of trig ratios and Inverse Trig ratios
Law of sines
Law of cosines
100
What is the Pythagorean Theorem formula?
100
How many types of special right triangles are there?
2
100
What are the three trig ratios?
sin opposite/hypotenuse
cosine = adjacent/hypotenuse
tangent = opposite/adjacent
100
What are the angle relationships for the law of sines?
AAS, ASA or SSA
100
What are the angle relationships for law of cosines?
SSS AND SAS
200
The sides of a triangle are 5, 8, and 8. What kind of triangle is it?
Acute
200
he ratio between the sides of any 30-60-90 triangle is ________:________:________.
200
A soccer player is 30 feet away from the goal line. He directly shoots the ball directly to the goal. The goal is eight feet high. What is the maximum angle of elevation?
14.9
200
Solve the triangle. m<b=45° a=28° b= 27°
x=38.2
200
triangle xyz= x=29m y=15m and <z = 122 degrees
What is the measure of side z?
39.08m
300
The sides of a triangle are 4, 9, and 9. What kind of triangle is it?
Acute
300
In a 45-45-90 special right triangle, there are two sides that are both 6 inches. What is the hypotenuse?
6 radical 2
300
You are on the deck of a cruise ship that is 375m above the water. You look down toward the ocean and see two orca whales. The angle of depression to the whales is 52 degrees and 53 degrees. How far is the first orca from the ship?
286.6m
300
Part of the marching band formed a triangle with the trumpet players on one side, the drum player on another side, and the saxophone player on the last side. The angle from by the trumpet and saxophone players is 65 degrees, the drum time is 20 feet long, and the saxophone line is eight feet long. Find the angle formed by trumpet and drum players
21.3
300
Two radar stations 2.5 miles apart are tracking an airplane. The straight-line distance between station A and 7 miles. The straight-line distance between station B and the plane is 9 miles. What is the elevation from station
31.9 degrees
400
Susan is trying to make her garden into a triangle. The current measurements she has for her backyard are 3 yards, 6 yards, and 9 yards. Is her backyard a triangle?
No, her backyard is not a triangle.
400
If the hypotenuse is 18 and the shortest side is 9, what is the longest side?
9 radical 3
400
A ladder leans against a wall, making an angle of 60 degrees with the ground. If the foot of the ladder is 5 feet away from the wall, how long is the ladder?
hypotenuse = 10 feet
400
If sin(46.5°)/x = sin(39.4°)/7, then x is?
8
400
If the sides of a triangle are 8 and 11 in units and the angle between them is 37 degrees, then the length of the third side is:
6.7
500
Lilly had drawn a triangle and claimed that the three numbers she used are Pythagorean triples. She used the numbers 10, 24, 26.
Yes
500
A 30-60-90 triangle has a hypotenuse of length 10. What are the lengths of the other two sides?
- Shorter side (opposite 30°): x = 5
- longer side (opposite 60°): x√3 = 5√3
500
A farmers’ co-operative wants to buy and install a grain auger. The auger would be used to lift grain from the ground to the top of a silo. The greatest angle of elevation that is possible for the auger is 35. The auger is 18 m long. What is the maximum height that the auger can reach?
10.3 m
500
Triangle PQR has <P = 63.5° and <Q = 51.2° and r = 6.3 cm. Find the other two sides and unknown angle.
<R = 65.3°, p = 6.21 cm and q = 5.40 cm
500
Given, in triangle abc, a = 32, b = 21 and angle between a and b is 40 degrees. Find the value of third side c.
20.87