solve for x.\n15 cm\n35°\nx\nx = ? cm\nround to the nearest hundredth.
solve for x.\n15 cm\n35°\nx\nx = ? cm\nround to the nearest hundredth.
Answer
Explanation:
Step1: Identify trigonometric ratio
In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the hypotenuse. Here, the angle is (35^\circ), the hypotenuse is (15) cm, and the side opposite to (35^\circ) is (x). So we use the sine function: (\sin(35^\circ)=\frac{x}{15}).
Step2: Solve for (x)
Multiply both sides of the equation by (15) to isolate (x): (x = 15\times\sin(35^\circ)). Calculate (\sin(35^\circ)) (using a calculator, make sure it's in degree mode). (\sin(35^\circ)\approx0.5736). Then (x = 15\times0.5736 = 8.604). Round to the nearest hundredth: (x\approx8.60).
Answer:
(8.60)