Here are the solutions for the missing lengths in the trigonometry worksheet. All answers are rounded to 3 significant figures as requested.
Section A
1)
* We have the hypotenuse (12 cm) and an angle ($35^\circ$). We need the opposite side ($x$).
* Use Sine: $\sin(35^\circ) = \frac{x}{12}$
* $x = 12 \times \sin(35^\circ)$
* $x \approx 6.8829...$
*
$x = 6.88$ cm
2)
* We have the hypotenuse (9 cm) and an angle ($67^\circ$). We need the adjacent side ($x$).
* Use Cosine: $\cos(67^\circ) = \frac{x}{9}$
* $x = 9 \times \cos(67^\circ)$
* $x \approx 3.5165...$
*
$x = 3.52$ cm
3)
* We have the adjacent side (16 cm) and an angle ($49^\circ$). We need the opposite side ($x$).
* Use Tangent: $\tan(49^\circ) = \frac{x}{16}$
* $x = 16 \times \tan(49^\circ)$
* $x \approx 18.405...$
*
$x = 18.4$ cm
4)
* We have the hypotenuse (17 cm) and an angle ($62^\circ$). We need the adjacent side ($x$).
* Use Cosine: $\cos(62^\circ) = \frac{x}{17}$
* $x = 17 \times \cos(62^\circ)$
* $x \approx 7.981...$
*
$x = 7.98$ cm
5)
* We have the adjacent side (5 cm) relative to the top angle ($27^\circ$). We need the opposite side ($x$).
* Use Tangent: $\tan(27^\circ) = \frac{x}{5}$
* $x = 5 \times \tan(27^\circ)$
* $x \approx 2.547...$
*
$x = 2.55$ cm
6)
* We have the hypotenuse (21 cm) and an angle ($33^\circ$). We need the adjacent side ($x$).
* Use Cosine: $\cos(33^\circ) = \frac{x}{21}$
* $x = 21 \times \cos(33^\circ)$
* $x \approx 17.612...$
*
$x = 17.6$ cm
---
Section B
1)
* We have the adjacent side (14 cm) and an angle ($15^\circ$). We need the hypotenuse ($x$).
* Use Cosine: $\cos(15^\circ) = \frac{14}{x}$
* $x = \frac{14}{\cos(15^\circ)}$
* $x \approx 14.495...$
*
$x = 14.5$ cm
2)
* We have the opposite side (19 cm) and an angle ($71^\circ$). We need the hypotenuse ($x$).
* Use Sine: $\sin(71^\circ) = \frac{19}{x}$
* $x = \frac{19}{\sin(71^\circ)}$
* $x \approx 20.113...$
*
$x = 20.1$ cm
3)
* We have the opposite side (5 cm) and an angle ($42^\circ$). We need the adjacent side ($x$).
* Use Tangent: $\tan(42^\circ) = \frac{5}{x}$
* $x = \frac{5}{\tan(42^\circ)}$
* $x \approx 5.553...$
*
$x = 5.55$ cm
4)
* We have the adjacent side (11 cm) relative to the top angle ($58^\circ$). We need the hypotenuse ($x$).
* Use Cosine: $\cos(58^\circ) = \frac{11}{x}$
* $x = \frac{11}{\cos(58^\circ)}$
* $x \approx 20.757...$
*
$x = 20.8$ cm
5)
* We have the opposite side (7 cm) relative to the top angle ($20^\circ$). We need the adjacent side ($x$).
* Use Tangent: $\tan(20^\circ) = \frac{7}{x}$
* $x = \frac{7}{\tan(20^\circ)}$
* $x \approx 19.230...$
*
$x = 19.2$ cm
6)
* We have the adjacent side (24 cm) and an angle ($36^\circ$). We need the hypotenuse ($x$).
* Use Cosine: $\cos(36^\circ) = \frac{24}{x}$
* $x = \frac{24}{\cos(36^\circ)}$
* $x \approx 29.666...$
*
$x = 29.7$ cm
Final Answer:
Section A:
1) 6.88 cm
2) 3.52 cm
3) 18.4 cm
4) 7.98 cm
5) 2.55 cm
6) 17.6 cm
Section B:
1) 14.5 cm
2) 20.1 cm
3) 5.55 cm
4) 20.8 cm
5) 19.2 cm
6) 29.7 cm
Parent Tip: Review the logic above to help your child master the concept of sohcahtoa worksheet with answers.
