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arley is building a model of a city map. In one part of the city, three roads form a right triangle, which Harley draws as triangle ABC, with the following measures: m∠B=90° and m∠A=30°. In his scale model, the hypotenuse of triangle ABC, AC¯¯¯¯¯¯¯¯, has a length of 817−−√ cm. What is the value of a (the length of BC¯¯¯¯¯¯¯¯)?

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Answer:


Step-by-step explanation:

  • ∠C= 180-(90+30)

            =60

(so this is a standard 30 60 90 triangle, it helps if you have a drawing)

  • AC=817cm
  • you'd have to use the angles since you don't have up to 2 sides
  • Using sin:

        sin=opp/hyp;

you're trying to find BC so it has to be either the opp or hyp. you know it's not hyp because you're already given that. the angle opposite BC is 30. That's how you know your angle's 30 and not 60

sin 30= BC/817  

BC=817sin 30

    =408.5 cm

  • using cos:

same here. hyp is given so adj has to be BC. the angle adjacent to BC is 60 so 60 is the angle here and not 30.

BC= 817 cos 60 (adj=cos×hyp)

    =408.5 cm


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