Question

Please answer KM, sin L, cos L, tan L, sin M, cos M, tan L.

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Find the value of KM

Using Pythagoras' Theorem,

$\begin{gathered} hypotenuse^2=opposite^2+adjacent^2 \\ hypotenuse=34,adjacent=16,opposite=? \end{gathered}$

By substitution,

$\begin{gathered} 34^2=opposite^2+16^2 \\ opposite^2=34^2-16^2 \\ opposite^2=900 \\ opposite=\sqrt{900}=30 \end{gathered}$

KM = 30

STEP 2: Find the required ratio

To get sin L:

$\begin{gathered} \sin\theta=\frac{opp}{hyp} \\ By\text{ substitution,} \\ \sin L=\frac{30}{34}=\frac{15}{17} \end{gathered}$

sin L = 15/17

To get cos L

$\begin{gathered} \cos\theta=\frac{adjacent}{hypotenuse} \\ \cos L=\frac{16}{34}=\frac{8}{17} \end{gathered}$

cos L = 8/17

To get tan L

$\begin{gathered} \tan\theta=\frac{opposite}{adjacent} \\ By\text{ substitution,} \\ \tan L=\frac{30}{16}=\frac{15}{8} \end{gathered}$

tan L = 15/8

STEP 3: Find the ratios for angle M

To get sin M

$\begin{gathered} \sin\theta=\frac{opp}{hyp} \\ By\text{ substitution,} \\ \sin M=\frac{16}{34}=\frac{8}{17} \end{gathered}$

sin M = 8/17

To get cos M

$\begin{gathered} \cos\theta=\frac{adj}{hyp} \\ By\text{ substitution,} \\ \cos M=\frac{30}{34}=\frac{15}{17} \end{gathered}$

cos M = 15/17

tan L has been done in Step 2

tan L = 15/8