Question

triangle trig: missing sides
solve for x. round to the tenth place. the questions are
different, but the answers match for partner a and b!
level i
1.
right triangle with 45° angle, adjacent side 12.7, opposite side x
2.
right triangle with 33° angle, hypotenuse x, adjacent side 13.4
3.
right triangle with 56° angle, hypotenuse 10, adjacent side x

triangle trig: missing sides
solve for x. round to the tenth place. the questions are
different, but the answers match for partner a and b!
level i
1.
right triangle with 48° angle, adjacent side 11.4, opposite side x
2.
right triangle with 35° angle, adjacent side 13.1, hypotenuse x
3.
right triangle with 26° angle, hypotenuse 19, adjacent side x

Explanation:

Step1: Identify left 1st triangle components

Right triangle: 45° angle, adjacent=12.7, x=opposite
$\tan(45^\circ)=\frac{x}{12.7}$
$x=12.7\times\tan(45^\circ)=12.7\times1=12.7$

Step2: Identify right 1st triangle components

Right triangle: 48° angle, adjacent=11.4, x=opposite
$\tan(48^\circ)=\frac{x}{11.4}$
$x=11.4\times\tan(48^\circ)\approx11.4\times1.1106\approx12.7$

Step3: Identify left 2nd triangle components

Right triangle: 33° angle, hypotenuse=13.4, x=opposite
$\sin(33^\circ)=\frac{x}{13.4}$
$x=13.4\times\sin(33^\circ)\approx13.4\times0.5446\approx7.3$

Step4: Identify right 2nd triangle components

Right triangle: 35° angle, adjacent=13.1, x=hypotenuse
$\cos(35^\circ)=\frac{13.1}{x}$
$x=\frac{13.1}{\cos(35^\circ)}\approx\frac{13.1}{0.8192}\approx16.0$

Step5: Identify left 3rd triangle components

Right triangle: 56° angle, hypotenuse=10, x=adjacent
$\cos(56^\circ)=\frac{x}{10}$
$x=10\times\cos(56^\circ)\approx10\times0.5592\approx5.6$

Step6: Identify right 3rd triangle components

Right triangle: 26° angle, hypotenuse=19, x=opposite
$\sin(26^\circ)=\frac{x}{19}$
$x=19\times\sin(26^\circ)\approx19\times0.4384\approx8.3$

Answer:

Left 1: 12.7
Right 1: 12.7
Left 2: 7.3
Right 2: 16.0
Left 3: 5.6
Right 3: 8.3