How do you solve the right triangle ABC given b=3, B=26?

Answer 1

See below.

I am assuming #B= 26# refers to the measurement of angle B in degrees.

Listing what we know already:

Angle A = #90^o-26^o= 64^o#

Angle B = #26^o#

Angle C = #90^o#

Side b = 3

Since we know all three angles and one side, we can use the Sine Rule to solve this:

#sinA/a=sinB/b=sinC/c#

We will use #sinA/a=sinB/b# , because we know angles A and B and we know b.

So:

#sin(64)/a=sin(26)/3=> a= (3sin(64))/sin(26)= 6.151# (3 .d.p)

By Pythagoras' Theorem:

#c^2 = a^2 +b^2#

#c^2= ((3sin(64))/sin(26))^2 + 3^2=> c=sqrt(((3sin(64))/sin(26))^2 + 3^2)= 6.844# ( 3 .d.p)

So we have solved the right angled triangle:

#a = 6.151# (3 .d.p)

#b= 3#

#c= 6.844# ( 3 .d.p)

#A = 64^o#

#B= 26^o#

#C = 90^o#

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Answer 2

To solve the right triangle ABC given b=3 and B=26 degrees:

  1. 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)
  2. 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).
  3. 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).
  4. 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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Answer from HIX Tutor

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.

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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