Question

label the sides and angle and calculate the missing values in the triangle: o = 1.04, θ = 38.9°

Explanation:

Step1: Use sine function

We know that $\sin\theta=\frac{O}{H}$, where $O = 1.04$ and $\theta = 38.9^{\circ}$.

Step2: Solve for $H$

$H=\frac{O}{\sin\theta}=\frac{1.04}{\sin(38.9^{\circ})}$.
Since $\sin(38.9^{\circ})\approx0.628$, then $H=\frac{1.04}{0.628}\approx1.66$.

Step3: Use tangent - cotangent relationship for $A$

We know that $\tan\theta=\frac{O}{A}$, so $A = \frac{O}{\tan\theta}$. Substituting $O = 1.04$ and $\theta=38.9^{\circ}$, and since $\tan(38.9^{\circ})\approx0.803$, then $A=\frac{1.04}{0.803}\approx1.30$.

Answer:

$A\approx1.30$, $H\approx1.66$