Trigonometric ratios: finding a side questions with answers

Questions

1. Question 1The unknown on top: multiply

   In the diagram, $\angle LMN = 90^\circ$. Find $x$, correct to 3 significant figures.

   Show the worked solution

   1. Step 1: Label the sides from the 63° angleFrom the 63° angle: the side $x$ m is the opposite and the side $15$ m is the hypotenuse.
   2. Step 2: Choose the ratio that uses those two sides (SOH CAH TOA) and write it down$\sin 63^\circ = \dfrac{x}{15}$
   3. Step 3: Make x the subject$x = 15 \sin 63^\circ$$= 13.3650\ldots$$= 13.4$ m (3 s.f.)
2. Question 2The unknown on top: multiply

   In the diagram, $\angle KLM = 90^\circ$. Find $x$, correct to 3 significant figures.

   Show the worked solution

   1. Step 1: Label the sides from the 38° angleFrom the 38° angle: the side $x$ m is the opposite and the side $20$ m is the adjacent.
   2. Step 2: Choose the ratio that uses those two sides (SOH CAH TOA) and write it down$\tan 38^\circ = \dfrac{x}{20}$
   3. Step 3: Make x the subject$x = 20 \tan 38^\circ$$= 15.6257\ldots$$= 15.6$ m (3 s.f.)
3. Question 3The unknown underneath: divide

   In the diagram, $\angle STU = 90^\circ$. Find $x$, correct to 3 significant figures.

   Show the worked solution

   1. Step 1: Label the sides from the 24° angleFrom the 24° angle: the side $x$ cm is the adjacent and the side $12$ cm is the opposite.
   2. Step 2: Choose the ratio that uses those two sides (SOH CAH TOA) and write it down$\tan 24^\circ = \dfrac{12}{x}$
   3. Step 3: Make x the subject$x = \dfrac{12}{\tan 24^\circ}$$= 26.9524\ldots$$= 27.0$ cm (3 s.f.)
4. Question 4The unknown underneath: divide

   In the diagram, $\angle DEF = 90^\circ$. Find $x$, correct to 3 significant figures.

   Show the worked solution

   1. Step 1: Label the sides from the 57° angleFrom the 57° angle: the side $x$ cm is the hypotenuse and the side $6$ cm is the opposite.
   2. Step 2: Choose the ratio that uses those two sides (SOH CAH TOA) and write it down$\sin 57^\circ = \dfrac{6}{x}$
   3. Step 3: Make x the subject$x = \dfrac{6}{\sin 57^\circ}$$= 7.1541\ldots$$= 7.15$ cm (3 s.f.)