Question

In right triangle ABC with the right angle at C, sin A= 2x + .1 and cos B = 4x - .7. Determine and state the vaule of x.

Answer 1

To find the value of x, we equate sin A to cos B because they represent complementary angles in the right triangle, leading to the solution x = 0.4.

Step-by-step explanation:

In right triangle ABC with the right angle at C, if sin A = 2x + 0.1 and cos B = 4x - 0.7, we use the fact that in a right triangle, angle A and angle B are complementary angles (they add up to 90 degrees). Therefore, sin A = cos B because the sine of an angle is equal to the cosine of its complement.

Setting the equations equal to each other gives us 2x + 0.1 = 4x - 0.7. Simplifying this equation, we subtract 2x from both sides and add 0.7 to both sides to obtain 2x = 0.8. Dividing both sides by 2 gives us x = 0.4.

Answer 2

Imagine
`\angle A` at the top of the triangle and
`\angle B` at the bottom. (or used the attached picture for reference)


`\sin A= (opposite)/(hypotenuse)`


`\cos B = (adjacent)/(hypotenuse)`

One thing to note, however, is that the side opposite
`\angle A` is the same side as the one adjacent to
`\angle B`! Thus
`\sin A=\cos B`.

Substitute these values for
`2x+0.1` and
`4x-0.7` and solve.


`4x-0.7=2x+0.1 \\ 4x=2x+0.8 \\ 2x=0.8\\ \boxed{x=0.4}`