# A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/4# and the angle between sides B and C is #pi/6#. If side B has a length of 2, what is the area of the triangle?

The area of the triangle is

Using the triangle and the sine rule

The triangle's area is

By signing up, you agree to our Terms of Service and Privacy Policy

To find the area of the triangle with sides (A), (B), and (C) given the lengths of sides (B) and the angles between them, we can use the law of sines to find the lengths of the other sides and then apply the formula for the area of a triangle.

Given:

- (B = 2)
- Angle between sides (A) and (B) is (\frac{\pi}{4}) (45 degrees)
- Angle between sides (B) and (C) is (\frac{\pi}{6}) (30 degrees)

Using the law of sines: [ \frac{A}{\sin(\frac{\pi}{6})} = \frac{2}{\sin(\frac{\pi}{4})} ] Solving for (A): [ A = 2 \cdot \frac{\sin(\frac{\pi}{6})}{\sin(\frac{\pi}{4})} ]

Similarly: [ \frac{C}{\sin(\frac{\pi}{6})} = \frac{2}{\sin(\frac{\pi}{6})} ] Solving for (C): [ C = 2 \cdot \frac{\sin(\frac{\pi}{6})}{\sin(\frac{\pi}{6})} ]

Now, we can use Heron's formula to find the area of the triangle: [ s = \frac{A + B + C}{2} ] [ \text{Area} = \sqrt{s(s - A)(s - B)(s - C)} ]

Substituting the values of (A), (B), and (C), we get: [ s = \frac{A + 2 + C}{2} ] [ \text{Area} = \sqrt{s(s - A)(s - 2)(s - C)} ]

Calculate (s) and substitute the values into the formula to find the area of the triangle.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- In triangle ABC, if #a = 8.75# centimeters, #c = 4.26# centimeters, and #m/_B# is #87°# what is the length of #b# to two decimal places?
- A triangle has sides A, B, and C. Sides A and B are of lengths #6# and #1#, respectively, and the angle between A and B is #(7pi)/8 #. What is the length of side C?
- Is (cotA+cotB)/(cotAcotB-1) equals to (cotAcotB-1)/(cotA+cotB) ?
- The sides of an isosceles triangle are 5, 5, and 7. How do you find the measure of the vertex angle to the nearest degree?
- What is the area of a triangle with sides of length 2, 4, and 5?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7