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

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