Pedal Triangle Properties

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Questions and Answers

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.

  • Inscribed triangle
  • Primitive Triangle
  • c. Pedal Triangle (correct)
  • Obtuse Triangl

Sin A cos B – cos A sin B is equivalent to:

  • Cos (A-B) (correct)
  • Tan (A-B)
  • Cot (A-B)
  • Sin (A-B)

How many degrees is 4800 mils?

  • 270 deg (correct)
  • 180 deg
  • 90 deg
  • 215 deg

The radius of the circle whose arc of length 15 cm makes an angle of ¾ radian at the center is:

<p>11.25 cm (B)</p> Signup and view all the answers

If sin A = 2.511x, cos A = 3.06x and sin²A = 3.939x, find the value of x.

<p>0.256</p> Signup and view all the answers

Solve for x if tan 3x = 5 tan x.

<p>20.705 deg (A)</p> Signup and view all the answers

If tan x = 1/2, tan y = 1/3, what is the value of tan (x + y)?

<p>1 (D)</p> Signup and view all the answers

The height of the monument is:

<p>33.51 m (B)</p> Signup and view all the answers

The triangle with minimum perimeter but maximum area inscribed in another triangle is known as:

<p>Pedal Triangle (A)</p> Signup and view all the answers

If the sides of the triangle are 2x + 3, x² + 3x + 3, and x² + 2x, find the greatest interior angle of the triangle.

<p>120 deg (D)</p> Signup and view all the answers

Given the sides of a triangle as 3m and 5m. The third side is:

<p>Between 3m and 8m (A)</p> Signup and view all the answers

Given triangle ABC in which A= 30°30', b= 100 m, and c = 200 m, find the length of side a.

<p>124.64 m (B)</p> Signup and view all the answers

An isosceles right triangle has a perimeter of 17.071. Compute the area of the triangle in square units.

<p>10.5 (B)</p> Signup and view all the answers

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.

<p>30.21 (C)</p> Signup and view all the answers

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.

<p>55.7 (C)</p> Signup and view all the answers

The angle which the line of sight to the object makes with the horizontal is above the eye of an observer.

<p>Angle of elevation (A)</p> Signup and view all the answers

The intersection of the medians of the triangle is called:

<p>Incenter (D)</p> Signup and view all the answers

Which of the following is not a property of a triangle?

<p>If the two sides are equal, the angles opposite are unequal. (B)</p> Signup and view all the answers

What is the sum of the squares of the sine and cosine of an angle?

<p>1 (D)</p> Signup and view all the answers

If the coverged sin θ = 0.134, what is the value of θ?

<p>30° (D)</p> Signup and view all the answers

The angle or inclination of ascend of a road having 8.25% grade is degrees?

<p>4.27 (B)</p> Signup and view all the answers

Which of the following cannot be an oblique angle?

<p>Right (B)</p> Signup and view all the answers

Evaluate arc cot[2 cos(arc sin 0.5)].

<p>60 deg (A)</p> Signup and view all the answers

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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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