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A triangle inscribed in a given triangle whose vertices
are the feet of the three perpendiculars to the sides
from the same point insie, the given triangle.
A triangle inscribed in a given triangle whose vertices are the feet of the three perpendiculars to the sides from the same point insie, the given triangle.
Sin A cos B – cos A sin B is equivalent to:
Sin A cos B – cos A sin B is equivalent to:
How many degrees is 4800 mils?
How many degrees is 4800 mils?
The radius of the circle whose arc of length 15 cm makes an angle of ¾ radian at the center is:
The radius of the circle whose arc of length 15 cm makes an angle of ¾ radian at the center is:
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If sin A = 2.511x, cos A = 3.06x and sin²A = 3.939x, find the value of x.
If sin A = 2.511x, cos A = 3.06x and sin²A = 3.939x, find the value of x.
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Solve for x if tan 3x = 5 tan x.
Solve for x if tan 3x = 5 tan x.
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If tan x = 1/2, tan y = 1/3, what is the value of tan (x + y)?
If tan x = 1/2, tan y = 1/3, what is the value of tan (x + y)?
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The height of the monument is:
The height of the monument is:
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The triangle with minimum perimeter but maximum area inscribed in another triangle is known as:
The triangle with minimum perimeter but maximum area inscribed in another triangle is known as:
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If the sides of the triangle are 2x + 3, x² + 3x + 3, and x² + 2x, find the greatest interior angle of the triangle.
If the sides of the triangle are 2x + 3, x² + 3x + 3, and x² + 2x, find the greatest interior angle of the triangle.
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Given the sides of a triangle as 3m and 5m. The third side is:
Given the sides of a triangle as 3m and 5m. The third side is:
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Given triangle ABC in which A= 30°30', b= 100 m, and c = 200 m, find the length of side a.
Given triangle ABC in which A= 30°30', b= 100 m, and c = 200 m, find the length of side a.
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An isosceles right triangle has a perimeter of 17.071. Compute the area of the triangle in square units.
An isosceles right triangle has a perimeter of 17.071. Compute the area of the triangle in square units.
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The area of an isosceles triangle is 36 m² with a 30° included angle of the two adjacent equal sides. Compute the perimeter of the triangle.
The area of an isosceles triangle is 36 m² with a 30° included angle of the two adjacent equal sides. Compute the perimeter of the triangle.
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To determine the width of a river, a surveyor measures a line AB 120 m long on one bank. To a point C on the other bank he determines the angle BAC = 48°36' and the angle ABC = 54°42'. Find the width of the river.
To determine the width of a river, a surveyor measures a line AB 120 m long on one bank. To a point C on the other bank he determines the angle BAC = 48°36' and the angle ABC = 54°42'. Find the width of the river.
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The angle which the line of sight to the object makes with the horizontal is above the eye of an observer.
The angle which the line of sight to the object makes with the horizontal is above the eye of an observer.
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The intersection of the medians of the triangle is called:
The intersection of the medians of the triangle is called:
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Which of the following is not a property of a triangle?
Which of the following is not a property of a triangle?
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What is the sum of the squares of the sine and cosine of an angle?
What is the sum of the squares of the sine and cosine of an angle?
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If the coverged sin θ = 0.134, what is the value of θ?
If the coverged sin θ = 0.134, what is the value of θ?
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The angle or inclination of ascend of a road having 8.25% grade is degrees?
The angle or inclination of ascend of a road having 8.25% grade is degrees?
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Which of the following cannot be an oblique angle?
Which of the following cannot be an oblique angle?
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Evaluate arc cot[2 cos(arc sin 0.5)].
Evaluate arc cot[2 cos(arc sin 0.5)].
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Study Notes
Trigonometry Formulas and Concepts
- The formula for the difference of two angles is: sin(A - B) = sin A cos B - cos A sin B
- The formula for the sum of two angles is: sin(A + B) = sin A cos B + cos A sin B
- The formula for the tangent of the difference of two angles is: tan(A - B) = (tan A - tan B) / (1 + tan A tan B)
- The formula for the tangent of the sum of two angles is: tan(A + B) = (tan A + tan B) / (1 - tan A tan B)
Angle of Elevation and Depression
- The angle of elevation is the angle between the line of sight and the horizontal when the object is above the observer's eye level.
- The angle of depression is the angle between the line of sight and the horizontal when the object is below the observer's eye level.
Solving Triangles
- In a right triangle, the Pythagorean theorem can be used to find the length of the hypotenuse: c² = a² + b²
- In a triangle, the law of cosines can be used to find the length of a side: c² = a² + b² - 2ab cos C
- In a triangle, the law of sines can be used to find the length of a side: a / sin A = b / sin B = c / sin C
Special Right Triangles
- A 30-60-90 triangle has angles of 30°, 60°, and 90°, and side lengths in the ratio of 1:√3:2
- A 45-45-90 triangle has angles of 45°, 45°, and 90°, and side lengths in the ratio of 1:1:√2
Inverse Trigonometric Functions
- The inverse sine function is defined as: sin⁻¹(x) = θ, where sin(θ) = x
- The inverse cosine function is defined as: cos⁻¹(x) = θ, where cos(θ) = x
- The inverse tangent function is defined as: tan⁻¹(x) = θ, where tan(θ) = x
Applications of Trigonometry
- Trigonometry can be used to solve problems involving right triangles, such as finding the height of a building or the distance to a ship at sea.
- Trigonometry can be used to solve problems involving oblique triangles, such as finding the area of a triangle or the length of a side.
- Trigonometry has many real-world applications, including physics, engineering, navigation, and computer graphics.
Important Values
- The value of sin(30°) is 1/2
- The value of cos(30°) is √3/2
- The value of tan(30°) is 1/√3
- The value of sin(45°) is 1/√2
- The value of cos(45°) is 1/√2
- The value of tan(45°) is 1
Unit Conversions
- 1 radian is equivalent to 180° / π
- 1 degree is equivalent to π / 180 radians
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Description
A quiz on the properties of a pedal triangle, formed by the feet of perpendiculars from a point inside a given triangle. Learn about this important concept in geometry!
