Questions: Home Aud

Solution Steps

In the right triangle BOR, we are given the angle BRO is \(90^\circ\) and the length BO is 57.3 km. We are also given the angle RBO is \(64.6^\circ\). We want to find BR. We can use the trigonometric ratio: \(\sin(\angle RBO) = \frac{BR}{BO}\) \(\sin(64.6^\circ) = \frac{BR}{57.3}\) \(BR = 57.3 \times \sin(64.6^\circ)\) \(BR \approx 57.3 \times 0.9036\) \(BR \approx 51.78\) km

In the right triangle BOR, we have \(\cos(\angle RBO) = \frac{OR}{BO}\) \(\cos(64.6^\circ) = \frac{OR}{57.3}\) \(OR = 57.3 \times \cos(64.6^\circ)\) \(OR \approx 57.3 \times 0.4258\) \(OR \approx 24.40\) km

We have EO = 98 km and OR = 24.40 km. We can use the trigonometric ratio in the triangle EOR. \(\cos(\angle EOR) = \frac{OR}{EO}\) \(\cos(\angle EOR) = \frac{24.40}{98}\) \(\cos(\angle EOR) \approx 0.2490\) \(\angle EOR = \arccos(0.2490)\) \(\angle EOR \approx 75.56^\circ\)

Final Answer