If a=6 in. and θ=45°, find the value of c. Round your answer to the nearest hundredth.

Answer 1

To find the value of c, we can use the formula for the length of the hypotenuse of a right triangle:

c = a / sin(θ)

Plugging in the given values of a = 6 in. and θ = 45°, we have:

c = 6 / sin(45°)

Using the sine of 45°, which is √2 / 2, we have:

c = 6 / (√2 / 2)

This can be simplified by multiplying the numerator and denominator by the conjugate:

c = (6 * 2) / (√2)

Simplifying further, we have:

c = 12 / √2

To rationalize the denominator, we multiply both the numerator and denominator by √2:

c = (12 / √2) * (√2 / √2)
c = (12√2) / 2
c = 6√2

Rounding this to the nearest hundredth, we get:

c ≈ 8.49 in.