Question

1. solve for the unknowns in the diagrams below.10 a) b)

Explanation:

Step1: Use tangent for part a

We know that $\tan(A)=\frac{a}{15}$, and $A = 35^{\circ}$. So $a = 15\times\tan(35^{\circ})$.
$a=15\times0.7002\approx10.503$

Step2: Use cosine for part a

We know that $\cos(A)=\frac{15}{c}$, and $A = 35^{\circ}$. So $c=\frac{15}{\cos(35^{\circ})}$.
$c=\frac{15}{0.8192}\approx18.31$

Step3: Use Pythagorean theorem for part b

In a right - triangle, by the Pythagorean theorem $x=\sqrt{25^{2}-12^{2}}$.
$x=\sqrt{(25 + 12)(25 - 12)}=\sqrt{37\times13}=\sqrt{481}\approx21.93$

Step4: Use cosine for part b

$\cos(\theta)=\frac{12}{25}$, so $\theta=\cos^{-1}(\frac{12}{25})\approx61.31^{\circ}$

Answer:

a) $a\approx10.50$, $c\approx18.31$
b) $x\approx21.93$, $\theta\approx61.31^{\circ}$