Question

In the triangle given below figure, calculate tan θ if ∠B = 90°, AB = 20 cm and AC = 40 cm.

Answer 1

Given: ∠B = 90°, AB = 20 cm, AC = 40 cm.

Step-wise calculation:

1. In right triangle ABC right-angled at B, AC is the hypotenuse, AB is one leg and BC is the other leg. 

By Pythagoras: `BC = sqrt(AC^2 - AB^2)` 

= `sqrt(40^2 - 20^2)`

= `sqrt(1600 - 400)`

= `sqrt(1200)`

= `20sqrt(3)`

2. Angle θ is at C.

So, `tan θ = ("Opposite side to"  θ)/("Adjacent side to"  θ)`

= `"AB"/"BC"` 

Therefore, `tan θ = 20/(20sqrt(3))`

= `1/sqrt(3)`

= `sqrt(3)/3`

`tan θ = sqrt(3)/3` (approximately 0.57735).