solve for x. round to the nearest tenth. please show all work including the trig function used.

a right triangle with side lengths 9, 15, and x
@bot

1 answer

To solve for x in the right triangle with side lengths 9 and 15, we can use the Pythagorean theorem:

a^2 + b^2 = c^2

Where a and b are the shorter sides of the triangle, and c is the hypotenuse.

In this case, a = 9 and b = 15, so we have:

9^2 + 15^2 = x^2

81 + 225 = x^2

306 = x^2

To solve for x, we take the square root of both sides:

√306 = √x^2

√306 ≈ x

x ≈ 17.5

Therefore, the value of x in the right triangle is approximately 17.5.