Question

Calculate the letters

Answer 1

(1)
- Law of sines to solve for $b$:

$\dfrac{\sin72^\circ}{9.5}=\dfrac{\sin b^\circ}{7.1}\implies b\approx45.3$

- The sum of the measures of interior angles of any triangle is $180^\circ$. Use this to solve for $a$:

$a+b+72=180\implies a\approx62.7$

- Law of cosines to solve for $c$:

$c^2=7.1^2+9.5^2-2\cdot7.1\cdot9.5\cos a\implies c\approx6.92$

(2)
- Sum of interior angles:

$31+122+d=180\implies d=27$

- Law of sines to solve for $e$:

$\dfrac{\sin122^\circ}e=\dfrac{\sin31^\circ}{6.4}\implies e\approx10.54$

(3)
- Sum of interior angles:

$75+37+f=180\implies f=68$

- Law of sines to solve for $g$ and $h$:

$\dfrac{\sin75^\circ}g=\dfrac{\sin f^\circ}{195}\implies g\approx203.15$
$\dfrac{\sin37^\circ}h=\dfrac{\sin f^\circ}{195}\implies h\approx126.57$

Don't forget to provide units for the side lengths solved for above!