How do you solve the right triangle ABC given b=3, B=26?
See below.
I am assuming
Listing what we know already:
Angle A = Angle B = Angle C = Side b = 3 Since we know all three angles and one side, we can use the Sine Rule to solve this: We will use So: By Pythagoras' Theorem: So we have solved the right angled triangle:
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To solve the right triangle ABC given b=3 and B=26 degrees:
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Use the given information to identify the sides and angles of the triangle:
- b = 3 (length of side opposite angle B)
- B = 26° (measure of angle B)
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Use the properties of right triangles to find the missing parts:
- Since B is given as 26°, angle A can be found using the fact that the sum of angles in a triangle is 180°. So, angle A = 90° - B = 90° - 26° = 64°.
- Angle C = 90° (since it's a right triangle).
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Use trigonometric ratios to find the missing side lengths:
- To find the length of side a, use the sine ratio: sin(A) = opposite / hypotenuse. sin(64°) = a / 3 a = 3 * sin(64°) ≈ 2.80 (rounded to two decimal places).
- To find the length of side c, use the Pythagorean theorem: c² = a² + b². c² = (2.80)² + (3)² c² ≈ 7.84 + 9 c² ≈ 16.84 c ≈ √16.84 ≈ 4.10 (rounded to two decimal places).
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Verify the solution:
- Check if the angles and side lengths satisfy the conditions of a right triangle.
Therefore, the solution for the right triangle ABC, given b=3 and B=26°, is:
- Side a ≈ 2.80 units
- Side c ≈ 4.10 units
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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