Harley is building a model of a city map.

Question

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 8 square root 17 cm. What is the value of a (the length of BC)?

Answer 1

We can make use of trig functions in order to find the length of BC. First, it would be helpful to draw a sketch of right triangle ABC. Once you do, you should be able to determine that the length of BC can be expressed as the sin A. Of course, the sine is defined as the opposite side over the hypotenuse. We know the length of the hypotenuse, which is 8√17. We can also compute the sin A, which is sin 30° = 1/2. If we let x = the length of the BC, then we have the following:

 

sin 30° = x/8√17

 

You should be able to handle it from here, Serenity.

Answer 2

We can use the law of sine.  Angle 90 degrees is opposite to the hypotenuse.  If you draw and label you right triangle correctly, you should the equation

 

sin(90) / AC = sin(30) / BC

 

BCsin(90) = ACsin(30)

 

BC = (1/2)AC

 

BC = (1/2)8√17

 

BC = 4√17 cm