**Shortcut 85:**

Using tanƟ

*Ɵ tan*

*0 0*

*30 [latex]1/\sqrt3 [/latex]*

*45 1*

*60 [latex] \sqrt3[/latex]*

*90 [latex]\infty [/latex]*

Question:

A man on a boat saw a tower of height 100m at an angle of 60o. What is the distance between the man and the tower?

Answer:

tanƟ = opp/adj

tan 60 = 100/x

√3 = 100/x

x= 100/√3

**Shortcut 86:**

Using Pythagoras theorem

*[latex] hyp^2=opp^2+adj^2[/latex]*

Question:

A man looks at the top of a tower which is 400m height. The minimum distance between him and top of the tower is 500m. What is the distance between him and the base of the tower?

Answer:

hyp2 = opp2 + adj2

5002 = 4002 + x2

x2 = 90000

x = 300 m