Question

Patty is 50 mi. due north of Todd. Emma is due east of Todd. Ifa line were drawn from Emma

to Todd and from Emma to Patty, the angle formed would measure 40 degrees. To the nearest
mile, how far is Emma from each person?

Answer 1

Correct choice is D

Explanation:

Consider right triangle PTE (Patty, Todd, Emma). In thistriangle PT=50 mi - the distanse between Patty and Todd, the distance between Patty and Emma PE and the distance between Emma and Todd ET are unknown. The angle PET has the measure of 40°. Then

• 
  `\sin 40^(\circ)=(PT)/(PE)\Rightarrow PE=(PT)/(\sin 40^(\circ))=(50)/(\sin 40^(\circ))\approx 78\ mi.`
• 
  `\tan 40^(\circ)=(PT)/(ET)\Rightarrow ET=(PT)/(\tan 40^(\circ))=(50)/(\tan 40^(\circ))\approx 60\ mi.`