Question

a right triangle has a hypotenuse of length 18 and an angle of 35°, with a side opposite this angle of length 4. a second right triangle also has an angle of 35°, with a hypotenuse of length 9. determine the length of the side opposite the 35° angle on the second triangle (2 point)

units

Explanation:

Step1: Define sine relationship

For a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$

Step2: Verify ratio for first triangle

$\sin(35^\circ) = \frac{4}{18} = \frac{2}{9}$

Step3: Apply ratio to second triangle

Let $x$ = opposite side of second triangle.
$\sin(35^\circ) = \frac{x}{9}$
Substitute $\sin(35^\circ) = \frac{2}{9}$:
$\frac{2}{9} = \frac{x}{9}$

Step4: Solve for x

Multiply both sides by 9:
$x = 2$

Answer:

2 units