solve triangle ABC which have angleA=25.25,angleB=60.51 and a=3.82..find c...,find b
Looks like a straightforward Sine Law problem
b/sinB = a/sinA
b/sin 60.51° = 3.82/sin 25.25°
you do the button pushing
3.6cm
6.7cm
To solve triangle ABC with angle A = 25.25°, angle B = 60.51°, and side a = 3.82, we will use the Law of Sines.
The Law of Sines states that in any triangle, the ratio of each side's length to the sine of its opposite angle is equal. Mathematically, it can be written as:
a/sin(A) = b/sin(B) = c/sin(C)
First, let's find angle C. Since the sum of angles in a triangle is always 180°, we can subtract the given angles A and B from 180° to find angle C:
C = 180° - A - B
C = 180° - 25.25° - 60.51°
C ≈ 94.24°
Now, we can use the Law of Sines to find side b and side c.
1. To find side b:
b/sin(B) = c/sin(C)
Plug in the given values:
b/sin(60.51°) = c/sin(94.24°)
Now, rearrange the equation to solve for b:
b = (sin(60.51°) * c) / sin(94.24°)
2. To find side c:
a/sin(A) = c/sin(C)
Plug in the given values:
3.82/sin(25.25°) = c/sin(94.24°)
Now, rearrange the equation to solve for c:
c = (sin(94.24°) * 3.82) / sin(25.25°)
Using a scientific calculator or trigonometric tables, calculate the values of b and c.