 # Practical examples of trigonometry

Example 1

An aircraft controller is told by a pilot that she wants to land. She is currently at 40,000ft and wants to know what angle of descent to take. The air traffic controller can see on the radar that her plane is 100,000ft away from the runway.

NOTE:

The radar only measures directly to the plane and back, therefore the 100,000ft is the hypotenuse. Start by writing down the name of the great trigger happy Indian war chief.

SOH CAH TOA

Work out which part of the triangle is which: We know the hypotenuse, we need theta  (the angle of descent), and opposite theta  is the opposite. The only formula with hypotenuse, theta and opposite in it is:

Choose             sin\ theta= (O)/(H)

Or                     sin\ theta= (Opposite)/(Hypoten\use)

sin\ theta= (40,000)/(100,000)

sin\ theta= 0.4

Put 0.4 in your calculator and then press inverse sin or (sin-1). This gives = 23.6

The pilot must descend at an angle of 23.6°

Example 2

A home owner is worried about whether a tree could fall onto her house. The house is 80 feet away, but she is not sure how tall the tree is. She asks the schoolkid next door to work it out for her. The kid measured the shadow length from the tree. She also had a large protractor and measured the angle as 50°. Then she did the following calculation:

She started by writing down the name of the great trigger happy Indian war chief.

SOH CAH TOA

She worked out which part of the triangle she needed: So she chooses tan\ theta= (O)/(A)

Or       tan\ theta= (Opposite)/(Adjacent)

tan\ 50= (O)/(A)

tan\ 50= (Opposite\ (height))/80

Opposite\ (height)=tan\ 50times80

(To find tan\ 50 put 50 into your calculator and then press the tan button. You should get 1.1917)

Opposite\ (height)=1.1917times80

Height=95.3\ feet

Yes, the house is in danger of being hit if the tree falls over.

Example 3

You have to build a ramp into a building, but it must be no more than a 5° angle, as required by building regulations. If the height of the door above the ground is 400mm, how long should the ramp be? Start by writing down the name of the great trigger happy Indian war chief.

SOH CAH TOA

Work out which part of the triangle is what: So we choose opposite and hypotenuse.

Choose    sin\ theta= (O)/(H)

Or            sin\ theta= (Opposite)/(Hypoten\use)

Or           sin\ 5= (400mm)/(Hypoten\use)

Rearrange the formula

Hypoten\use=(400mm)/sin5

On a calulator press 5 and then sin and you get 0.08715.

Hypoten\use=(400mm)/0.08715

Hypoten\use=4589mm\ \ or\ \ 4.6m  (to the nearest 0.1m)