Pythagorean Theorem
When can you use the Pythagorean Theorem.
When solving for a missing side and you have 2 sides already.
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
In a 30-60-90 triangle, the short leg is 1. How long is the long leg AND the hypotenuse? Your answers should be in simplified radical form.
Long leg is √3.
Hypotenuse is 2.
What acronym can you use to remember the three trigonometric ratios? Give the correct spelling.
SOHCAHTOA
What kind of angles look downwards from a horizontal line of sight?
Angles of Depression
What kind of triangle has side lengths 5 ft, 6 ft, and 10 ft? Acute, Right, or Obtuse?
An obtuse triangle.
Is a 45-45-90 Triangle always Equilateral, Isosceles, or Scalene?
Isosceles
In a 30-60-90 triangle, the hypotenuse is 4 ft. What is the length of the short leg?
2 ft
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.
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
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
In a 45-45-90 triangle, one of the legs is 3 ft long. How long is the hypotenuse? Your answer should be in simplified radical form.
3√2 ft
Is a 30-60-90 triangle equilateral, isosceles, or scalene?
scalene
Which trigonometric ratio should you use if you know the opposite side and are trying to find the length of the adjacent side?
Tangent
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
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 ft
In a 45-45-90 triangle, one of the legs is 51 cm. How long is the other leg and the hypotenuse? Your answers should be in simplified radical form.
other leg = 51 cm
hypotenuse = 51√2 cm
In a 30-60-90 triangle, the long leg is 6 meters. What is the length of the short leg in simplest radical form?
2√3 meters
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
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 12 and one of the legs is 6. How long is the other leg?
Answer in simplest radical form and rounded to the nearest tenth.
6√3
approx 10.4
If a square has a diagonal of length 16 meters, what is the side length of the square rounded to the nearest tenth of a meter?
11.3 meters
If the long leg of a 30-60-90 triangle is 11 cm, what is the length of the hypotenuse in simplest radical form?
22√3/3 cm
If the side opposite a 48 degree angle is 15 cm, what is the adjacent side length? Round to the nearest tenth.
13.5 cm
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