NEED HELP!! Trigonometry questions
1 answer:
Answer:
Step-by-step explanation:
Question 1: Assumption: This is a 30-60-90 triangle.
Remember that the sides of a 30-60-90 triangle are in the ratio 1:√3:2
The side opposite the 90° angle is 16, so the side opposite the 30° angle is 16/2 = 8
x = 8 units.
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Question 2: Assumption: This is an isosceles triangle.
Draw the altitude to the vertex angle and you get a 30-60-90 triangle.
The side opposite the 90° angle has length 22, so the side opposite the 30° angle has length 11.
x/2 = 11
x = 22 units
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Question 3: Assumption: This is a 45-45-90 triangle.
The sides of a 45-45-90 triangle are in the ratio 1:1:√2
The sides opposite the 45° angles are 19 and x.
x = 19
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Question 4: Assumption: This is an isosceles triangle.
x = 13 units
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Question 5: Assumption: This is a right triangle.
sin(54°) = x/45
x = 45sin(54°) ≅ 36.4 units
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Question 6: Assumption: This is a right triangle.
sin(35°) = z/23
z = 23sin(35°) ≅ 13.2 units
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<h3>Answer:</h3>
Equation of the ellipse = 3x² + 5y² = 32
<h3>Step-by-step explanation:</h3><h2>Given:</h2>- The centre of the ellipse is at the origin and the X axis is the major axis
- It passes through the points (-3, 1) and (2, -2)
- The equation of the ellipse
The equation of an ellipse is given by,
Given that the ellipse passes through the point (-3, 1)
Hence,
Cross multiplying we get,
- 9b² + a² = 1 ²× a²b²
- a²b² = 9b² + a²
Multiply by 4 on both sides,
- 4a²b² = 36b² + 4a²------(1)
Also by given the ellipse passes through the point (2, -2)
Substituting this,
Cross multiply,
- 4b² + 4a² = 1 × a²b²
- a²b² = 4b² + 4a²-------(2)
Subtracting equations 2 and 1,
- 3a²b² = 32b²
- 3a² = 32
- a² = 32/3----(3)
Substituting in 2,
- 32/3 × b² = 4b² + 4 × 32/3
- 32/3 b² = 4b² + 128/3
- 32/3 b² = (12b² + 128)/3
- 32b² = 12b² + 128
- 20b² = 128
- b² = 128/20 = 32/5
Substituting the values in the equation for ellipse,
Multiplying whole equation by 32 we get,
3x² + 5y² = 32
<h3>Hence equation of the ellipse is 3x² + 5y² = 32</h3>