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. (1 point)
units
check answer
remaining attempts : 3

Explanation:

Step1: Recall sine formula

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

Step2: Identify values

Here, $\theta = 35^\circ$, hypotenuse $= 9$. Let opposite side be $x$.

Step3: Solve for x

Using $\sin(35^\circ) = \frac{x}{9}$, so $x = 9 \times \sin(35^\circ)$.
Calculate $\sin(35^\circ) \approx 0.5736$, then $x \approx 9 \times 0.5736 \approx 5.16$.

Answer:

Approximately 5.16 units (or more precise value based on calculator's $\sin(35^\circ)$)