SOH CAH TOA PROBLEMS SOLVING RIGHT TRIANGLES. To SOLVE A TRIANGLE means to know all three sides and all three angles. For example: C 12 cm x 40° A yB.

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Presentation transcript:

SOH CAH TOA PROBLEMS SOLVING RIGHT TRIANGLES

To SOLVE A TRIANGLE means to know all three sides and all three angles. For example: C 12 cm x 40° A yB But this problem can’t be solved using Pythagorean theorem because both x and y sides are unknown…

SOH CAH TOA, and of course trig functions, can help you….. Let’s listen! SOH CAH TOA

Sohcahtoa is an easy way to remember how Sine, Cosine and Tangent work: Soh... Sin( ɵ ) = Opposite / Hypotenuse...cah... Cos( ɵ ) = Adjacent / Hypotenuse...toa Tg( ɵ ) = Opposite / Adjacent

Firstly, the names Opposite, Adjacent and Hypotenuse come from the right triangle " Opposite" is opposite to the angle θ "Adjacent" is adjacent (next to) to the angle θ "Hypotenuse" is the longest one

Pay attention to what is the angle you know and put “opposite” in front of it. For example: C 12 cm 40° A B What is the opposite (side) ? And the adjacent? opposite adjacent

Then you will choose soh, cah, or toa depending on what information you know. In this case you have hypotenuse and an angle so you can use soh and work out the opposite: opposite adjacent A B C 12 cm 40°

…or you can use cah and work out the adjacent: opposite adjacent A B C 12 cm 40°

Finally, if you have an angle and one of the two catheti you will find the other side using toa : ? 10 cm A B C 40°

Exercises:

SOHCAHTOA around the world

Problem : An airplane flies 3 degrees off course for 400 km, how far away from the correct path is the plane? correct path 3° 400 km ? You know hypotenuse, the angle ɵ and you have to find the opposite.