Podcast
Questions and Answers
In a right triangle, which side is always opposite the right angle?
In a right triangle, which side is always opposite the right angle?
- Hypotenuse (correct)
- Adjacent
- Opposite
- Leg
Considering a specific angle in a right triangle, what is the ratio of the adjacent side to the hypotenuse?
Considering a specific angle in a right triangle, what is the ratio of the adjacent side to the hypotenuse?
- Secant
- Tangent
- Cosine (correct)
- Sine
What must be the value of angle A if a triangle has angles measuring 45°, A°, and 90°?
What must be the value of angle A if a triangle has angles measuring 45°, A°, and 90°?
- 45° (correct)
- 90°
- 30°
- 60°
What is the exact combined value of $\sin(30^\circ)$ and $\cos(60^\circ)$?
What is the exact combined value of $\sin(30^\circ)$ and $\cos(60^\circ)$?
Given a scenario where someone is looking at the top of a tall Christmas tree, which concept does this illustrate?
Given a scenario where someone is looking at the top of a tall Christmas tree, which concept does this illustrate?
If $m\angle A = 30^\circ$ represents an angle of elevation and $m\angle D = 40^\circ$ represents another angle, what is the combined measure of the angle of elevation?
If $m\angle A = 30^\circ$ represents an angle of elevation and $m\angle D = 40^\circ$ represents another angle, what is the combined measure of the angle of elevation?
Amor places a 4.5 m ladder against a wall to reach a window 4 m above the ground. What is closest to the angle the ladder forms with the ground?
Amor places a 4.5 m ladder against a wall to reach a window 4 m above the ground. What is closest to the angle the ladder forms with the ground?
Consider a scenario where Lowell's House, Lorena's House, and Precious' House form a right triangle. If the distance between Lowell and Lorena is 10 meters, and the angle at Lowell's house ($m\angle A$) is 40°, which trigonometric ratio will help determine the distance between Lorena's and Precious' houses?
Consider a scenario where Lowell's House, Lorena's House, and Precious' House form a right triangle. If the distance between Lowell and Lorena is 10 meters, and the angle at Lowell's house ($m\angle A$) is 40°, which trigonometric ratio will help determine the distance between Lorena's and Precious' houses?
Given two sides of a triangle are 5 and 6, and the angle in between is 50°, what formula should you use to find the third side?
Given two sides of a triangle are 5 and 6, and the angle in between is 50°, what formula should you use to find the third side?
Martha wants to build a fence around her triangular garden. One side is 28.32 meters with angles of 43 and 59 degrees at each end. What calculation is needed to determine the garden's perimeter?
Martha wants to build a fence around her triangular garden. One side is 28.32 meters with angles of 43 and 59 degrees at each end. What calculation is needed to determine the garden's perimeter?
Flashcards
Trigonometry
Trigonometry
The study of triangle measurements.
Hypotenuse
Hypotenuse
The side of a right triangle opposite the right angle.
Sine (sin)
Sine (sin)
The ratio of the opposite side to the hypotenuse.
Cosine (cos)
Cosine (cos)
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Tangent (tan)
Tangent (tan)
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Angle of Elevation
Angle of Elevation
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Angle of Depression
Angle of Depression
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Horizontal line
Horizontal line
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Line of Sight
Line of Sight
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Alternate Interior Angles
Alternate Interior Angles
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Study Notes
- Trigonometry refers to the study of triangle measurements.
- The hypotenuse is the side of the triangle that is always opposite the right angle.
- The sine of an angle is the ratio of the opposite side to the hypotenuse.
- The cosine of an angle is the ratio of the adjacent side to the hypotenuse.
- A 45°-45°-90° angle is a special angle in a right triangle.
- The value of cos 60° is 1/2.
- The exact value of sin 30 + cos 60 is 1.
- The exact value of sec 60 + sin 30 is 2 1/2.
- Given a triangle ABC with sides 5 ft, 12 ft, and 13 ft, the hypotenuse is AC.
- The side adjacent to ∠B in the triangle is BC.
- The value of sin B in the triangle is 5/13.
- The value of tan A in the triangle is 12/5.
- A 30°-60°-90° angle is a special angle in a right triangle.
- With respect to an emoticon looking at a star, the angle of elevation is ∠A.
- With respect to an emoticon looking at a star, the angle of depression is ∠D.
- The line segment between ∠B and ∠C represents the horizontal line.
- The line segment between the emoticon and the star represents the line of sight.
- If m∠A = 30° and m∠D = 40°, the measure of the angle of elevation is 70°.
- If m∠A = 30° and m∠D = 40°, the measure of the angle of depression is 70°.
- Lowell looking at a star on a Christmas tree illustrates the angle of elevation.
- Luzviminda on top of a tower watching a boat leaving the port illustrates the angle of depression.
- The angle of elevation and depression represent alternate interior angles formed by a parallel lines cut by a transversal.
- If Amor places a 4.5 m ladder against the side of her house to reach a window that is 4 m above the ground, the angle that the ladder makes with the ground is 63°.
- Given a triangle where h = 10 cm and I = 16 cm, and one angle is 67°, the measure of ∠H is 36.25°.
- Given a triangle where h = 10 cm and I = 16 cm, and one angle is 67°, the measure of ∠G is 77.88°.
- Given a triangle where h = 10 cm and I = 16 cm, and one angle is 67°, side g measures 18.24.
- "IH" has the shortest measurement.
- In a given triangle with sides 5 and 6, and an angle of 50°, the value of c is 3.88.
- In a triangle with sides of length 4 and 5 and an included angle of 50°, the length of the third side (a) is approximately 3.88.
- Given the figures, in a triangle with a 30° angle, the value of b is 13.26.
- Given a triangle with sides 5, 6, and 7, the measure of angle C is 81.21°.
- If Martha's triangular garden has one side of 28.32 meters and angles of 43 and 59 degrees at the ends of this side, then the measure of the shorter side is 20.13 m.
- If Martha's triangular garden has one side of 28.32 meters and angles of 43 and 59 degrees at the ends of this side, then the measure of the longest side is 32.32 m.
- If Martha's triangular garden has one side of 28.32 meters and angles of 43 and 59 degrees at the ends of this side, then the perimeter of the fence is 83.17 m.
- If Daniel and Kathryn paid PhP17.50 and PhP17.00 respectively, and Kathryn's angle measures 63 degrees, the angle that corresponds to Daniel's house is 59.95 degrees.
- If Daniel and Kathryn paid PhP17.50 and PhP17.00 respectively, and Kathryn's angle measures 63 degrees, the distance between Kathryn and Daniel's House is 3.3 km
- If Daniel and Kathryn paid PhP17.50 and PhP17.00 respectively, and Kathryn's angle measures 63 degrees, the total estimated fare if you want to ride a tricycle from Daniel's House to Studio A then to Kathryn's is PhP51.00.
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