Question

What is the tangent ratio of angle BCD?

A) 10√3 over 20
B) 10√3 over 10
C) 10 over 10√3
D) 10 over 20√3

Answer 1

B)

Explanation:

given the 2 angles of 60°, that makes the 3rd angles also 60° (remember, the sum of all angles in a triangle is always 180°).

and that makes the triangle an equilateral triangle (all 3 sides are equally long : 20).

BD = sin(60)×20

CD = cos(60)×20

tan(60) = sin(60)/cos(60) = sin(60)×20/(cos(60)×20)

CD = 20/2 = 10

for BD we need Pythagoras

20² = BD² + 10²

400 = BD² + 100

300 = BD²

BD = sqrt(300) = sqrt(4×75) = sqrt(4×25×3) =

= 2×5×sqrt(3) = 10×sqrt(3)

so,

tan(60) = BD/CD = 10×sqrt(3) / 10

which is sqrt(3), by the way.