use inver tangent ratio to solve this useing angles 20 and 25 what is vertex b

Answer 1

To solve for the vertex B using the inverse tangent ratio, we need to consider the right triangle formed by the angles 20 and 25.

Let's first label the sides of the triangle:
- The side opposite angle 20 is side b
- The side adjacent to angle 20 is side a
- The hypotenuse of the triangle is side c

Now, we can use the tangent ratio:
tan(20°) = b/a

Rearranging the equation to solve for side b:
b = a * tan(20°)

Similarly, for angle 25:
tan(25°) = a/c

Rearranging the equation to solve for side a:
a = c * tan(25°)

Now that we have expressions for side a and side b in terms of c, we can combine them with the equation b = a * tan(20°) to get:
b = c * tan(25°) * tan(20°)

Since b is the opposite side to angle B in the right triangle, we can find angle B by taking the arctan of the ratio b/c:
B = arctan(b/c)
B = arctan(tan(25°) * tan(20°))

Calculating the value of B:
B ≈ arctan(tan(25°) * tan(20°))
B ≈ arctan(tan(0.4364) * tan(0.3639))
B ≈ arctan(0.4364 * 0.3639)
B ≈ arctan(0.1589)
B ≈ 8.97°

Therefore, the vertex B in the triangle with angles 20° and 25° is approximately 8.97°.