M20 | Maths Made Easy

M20

Question: Find the size of the angle marked q to 1 d.p.

 

Answer: The two sides we’re concerned with are the hypotenuse and the opposite (to the angle) – O and H. Therefore, we want the ‘SOH’ part of ‘SOHCAHTOA’, so will be using sin. We have O=13,H=15, and the angle is q, so we get

\sin(q)=\dfrac{O}{H}=\dfrac{13}{15}

Then, to get q, we have to apply the inverse sin function: \sin^{-1} to both sides. It cancels out the sin on the left-hand side, and we get

q=\sin^{-1}\left(\dfrac{13}{15}\right)

Finally, putting this into the calculator we get

q=60.0735...=60.1\degree\text{ (1dp)}