Question

Find g.

60°
6 km
9
30°
Write your answer in simplest radical form.
kilometers

Answer 1

4√3 or 6.9282Km

Explanation:

Let the triangle be ABC, right angled at B

Angle A = 60 degrees

Angle C = 30 degrees

BC = 6 km

To find AB,

Tan30°=AB/BC

Now we know that tan30° is 1/√3 so,

1/√3 = AB / 6

6/√3 = AB

6√3/3 =AB

2√3 = AB

Now we have the value of two sides so we can use the Pythagoras Theorem to find the hypotenuse, which is g

AB² + BC² = AC²

(2√3)² + 6² = g²

12 + 36 = g²

48 = g²

Therefore g = √48km or 4√3km or 6.9282Km