Harley 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 32.9848450049 cm. What is the value of a (the length of BC)?

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tallinn tallinn · Answer 1 · 2019-11-12T11:40:29+01:00

Answer:

Value of a ( Length of BC) = 16.4925cm

Step-by-step explanation:

Given: In right Δ ABC, m∠B = 90°, and m∠A = 30° and Hypotenuse AC = 32.9848450049 cm.

To find: Length of BC (value of a) = ?

Sol: In right Δ ABC,

m∠A + m∠B + m∠C = 180° ( sum of angles of a triangle)

30° + 90° + m∠C = 180°

m∠C = 180° - 120° = 60°

Now Using trigonometry ratios, in right Δ ABC,

[tex]Cos C = \frac{side\ adjacent\ to\angle C}{hypotenuse}[/tex]

[tex]Cos 60 = \frac{BC}{AC}[/tex]

[tex]\frac{1}{2} = \frac{a}{32.985}[/tex] (∵ cos 60° = 1/2 and [tex]32.9848450049 \approx\ 32.985)[/tex]

[tex]2a = 32.985[/tex]

[tex]a = 16.4925[/tex]

Therefore, value of a ( Length of BC) = 16.4925 cm.