Question

label the sides and angle and calculate the missing values in the triangle: o = 1.63 h = 2.64

Explanation:

Step1: Calculate angle θ

Use the sine - function $\sin\theta=\frac{O}{H}$. Given $O = 1.63$ and $H=2.64$, then $\sin\theta=\frac{1.63}{2.64}$.
$\theta=\sin^{- 1}(\frac{1.63}{2.64})$
$\theta=\sin^{-1}(0.6174)$
$\theta\approx38.1^{\circ}$

Step2: Calculate side A

Use the Pythagorean theorem $A=\sqrt{H^{2}-O^{2}}$.
$A=\sqrt{2.64^{2}-1.63^{2}}=\sqrt{(2.64 + 1.63)(2.64 - 1.63)}=\sqrt{4.27\times1.01}=\sqrt{4.3127}\approx2.08$

Answer:

$A\approx2.08$, $\theta\approx38.1^{\circ}$