Question

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)?

Answer 1

Value of a ( Length of BC) = 16.4925cm

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,

`Cos C = (side\ adjacent\ to\angle C)/(hypotenuse)`

`Cos 60 = (BC)/(AC)`

`(1)/(2) = (a)/(32.985)` (∵ cos 60° = 1/2 and
`32.9848450049 \approx\ 32.985)`

`2a = 32.985`

`a = 16.4925`

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