Pythagorean Thm and Converse
DOUBLE POINT QUESTION!
What kind of triangle has side lengths 5 ft, 6 ft, and 10 ft? Acute, Right, or Obtuse?
An obtuse triangle.
If 45-45-90 triangle has a hypotenuse of 4√2 then what is the length of one of the legs of that triangle?
4
Which trigonometric ratio should you use if you know the opposite side and are trying to find the length of the adjacent side?
Tangent
The angle of elevation of the top of a flag pole from a point 20m from its base is 32°. Find the height of the pole. Round to the nearest tenth.
12.5m
DOUBLE POINT QUESTION!
Name 2 Pythagorean Triples.
Answers vary.
A right triangle has a leg length of 7 ft and a hypotenuse length of 25 ft. What is the length of the other leg?
24 feet
In a 30-60-90 triangle, the hypotenuse is 4 ft. What is the length of the short leg?
2
If the side adjacent to an angle is 5 cm, and the hypotenuse is 13 cm, what is the angle measure to the nearest degree?
67 degrees
DOUBLE POINT QUESTION!
A sailor sights a fortress on top of a 45m cliff from his position 1.6 km out from the base of the cliff. What is the angle of elevation from the sailor to the fortress?
Round to the nearest whole number.
21m
Inverse cosine
If a ladder is leaning against a wall so that it reaches a height of 12 feet, and the base of the ladder is 5 feet from the base of the wall, how long is the ladder?
13 Feet
DOUBLE POINT QUESTION!
In a 30-60-90 triangle, the long leg is 6 meters. What is the length of the middle leg in simplest radical form?
3√3
In a right triangle, the hypotenuse is 10 in. How long is the side opposite the 32 degree angle? Round to the nearest tenth.
5.3 in
While flying a kite, Linda lets out 45 feet of string and anchors it to the ground. She determines that the angle of elevation of the kite is 58 degrees. What is the height of the kite from the ground? Round to the nearest tenth.
38.2 feet
In a right triangle, the hypotenuse is 10, and the side opposite of an acute angle is 5. What is the measure of the acute angle?
30 degrees
Scott is using a 12-foot ramp to help load furniture into the back of a moving truck. If the back of the truck is 3.5 feet from the ground, what is the horizontal distance from where the ramp reaches the ground to the truck.
Round to the nearest tenth place.
11.5
If a square has a diagonal of length 16 meters, what is the side length of the square written in radical form
8√2 meters
DOUBLE POINT QUESTION!
If the side opposite a 48 degree angle is 15 cm, what is the adjacent side length? Round to the nearest tenth.
13.5
Philip observes a ship out to sea from his position at the top of a 42m high lighthouse. The angle of depression to the ship is 23°. Find the distance from the ship to the base of the lighthouse.
98.9m
DOUBLE POINT QUESTION!
A slide has an angle of depression of 58°. If the slide is 12.3m long, find the horizontal distance that the slide reaches .
6.52m